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In this paper, we study LCD BCH codes over the finite field GF(q) with two types of lengths n, where n = q(l) + 1 and n = (q(l) + 1)/(q + 1). Several classes of LCD BCH codes are given and their parameters are determined or bounde...
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In this paper, we study LCD BCH codes over the finite field GF(q) with two types of lengths n, where n = q(l) + 1 and n = (q(l) + 1)/(q + 1). Several classes of LCD BCH codes are given and their parameters are determined or bounded by exploring the cyclotomic cosets modulo n. For n = q(l) + 1, we determine the dimensions of the codes with designed distance delta, where q(left perpendicular l+1/2 right perpendicular) + 1 收起
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In this paper, we construct quantum synchronizable codes (QSCs) based on the sum and intersection of cyclic codes. Further, infinite families of QSCs are obtained from BCH and duadic codes. Moreover, we show that the work of Fujiw...
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In this paper, we construct quantum synchronizable codes (QSCs) based on the sum and intersection of cyclic codes. Further, infinite families of QSCs are obtained from BCH and duadic codes. Moreover, we show that the work of Fujiwara (Phys. Rev. A 87(02): 23-44, 2013) can be generalized to repeated root cyclic codes such that QSCs are always obtained, which is not the case with simple root cyclic codes. The usefulness of this extension is illustrated via examples of infinite families of QSCs from repeated root duadic codes. Finally, QSCs are constructed from the product of cyclic codes.
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Additive multivariate codes over F_4 (the Galois field with 4 elements) are a natural extension of additive cyclic and abelian codes. A complete description of such codes when the length is odd was presented in. In this paper we s...
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Additive multivariate codes over F_4 (the Galois field with 4 elements) are a natural extension of additive cyclic and abelian codes. A complete description of such codes when the length is odd was presented in. In this paper we study some properties of this family of codes in the case when the length is even (modular case) and the number of variables is two (bivariate codes).
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Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and cloud storage systems about nine years ago. A lot of progress on the study of LRCs has been made by now. However, there is a lack of genera...
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Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and cloud storage systems about nine years ago. A lot of progress on the study of LRCs has been made by now. However, there is a lack of general theory on the minimum locality of linear codes. In addition, the minimum locality of many known families of linear codes has not been studied in the literature. Motivated by these two facts, this paper develops some general theory about the minimum locality of linear codes, and investigates the minimum locality of a number of families of linear codes, such as q-ary Hamming codes, q-ary Simplex codes, generalized Reed-Muller codes, ovoid codes, maximum arc codes, the extended hyperoval codes, and near MDS codes. Many classes of both distance-optimal and dimension-optimal LRCs are presented in this paper. To this end, the concepts of linear locality and minimum linear locality are specified. The minimum linear locality of many families of linear codes are settled with the general theory developed in this paper.
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In this paper we focus on two generalizations of the notion of cyclicity of codes: polycyclic codes and sequential codes. We establish a duality between these two generalizations and also show connections between them and other we...
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In this paper we focus on two generalizations of the notion of cyclicity of codes: polycyclic codes and sequential codes. We establish a duality between these two generalizations and also show connections between them and other well-known generalizations of cyclicity such as the notions of negacyclicity and constacyclicity. In particular, it is shown that a code C is sequential and polycyclic if and only if C and its dual C? are both sequential if and only if C and its dual C? are both polycyclic. Furthermore, any one of these equivalent statements characterizes the family of constacyclic codes.
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This correspondence revisits the idea of constructing a binary [mn,mk] code from an [n,k] code over F/sub 2//sup m/ by concatenating the code with a suitable basis representation of F/sub 2//sup m/ over F/sub 2/. We construct two ...
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This correspondence revisits the idea of constructing a binary [mn,mk] code from an [n,k] code over F/sub 2//sup m/ by concatenating the code with a suitable basis representation of F/sub 2//sup m/ over F/sub 2/. We construct two nonequivalent examples of doubly even self-dual binary codes of length 160 which turn out to be of minimum distance 24. This improves the lower bound for this class of codes, whereas the upper bound is given by 28. The construction at hand seems to be of interest beyond this particular example.
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Cyclic codes are an interesting class of linear codes due to their efficient encoding and decoding algorithms. Bose-Chaudhuri-Hocquenghem (BCH) codes which form a significant subclass of cyclic codes are important in both theory a...
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Cyclic codes are an interesting class of linear codes due to their efficient encoding and decoding algorithms. Bose-Chaudhuri-Hocquenghem (BCH) codes which form a significant subclass of cyclic codes are important in both theory and practice since they have good error-correcting capabilities and have been widely used in communication systems, storage devices, and so on. Quantum codes with good parameters can be also constructed from BCH codes. In this paper, we construct q-ary quantum codes of length q2m-1 rho using constacyclic BCH codes with order rho and cyclic BCH codes, respectively, where rho divides q+1, q is a prime power and m is a positive integer. By comparing the obtained quantum codes, we get that constacyclic BCH codes are a better resource in constructing quantum codes than cyclic BCH codes in general. Compared with the quantum codes available in Aly et al. (IEEE Trans Inf Theory 53(3): 1183-1188, 2007) and Zhang et al. (IEEE Access 4:36122, 2018), the quantum codes in our schemes have better parameters. In particular, we extend some known results in Kai et al. (Int J Quantum Inf 16(7):1850059, 2018), La Guardia (Phys Rev A 80(4):042331, 2009), Li et al. (Quantum Inf Comput 12:0021-0035, 2013), Lin (IEEE Trans Inf Theory 50(3):5551-5554, 2004), Tang et al. (IEICE Trans Fund E102-A(1):303-306, 2019), Wang and Zhu (Quantum Inf Process 14(3):881-889, 2015), Yuan et al. (Des Codes Cryptogr 85(1):179-190, 2017) to more general case.
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Let p be an odd prime, and k be an integer such that gcd(k,p) = 1. Using pairwise orthogonal idempotents gamma(1), gamma(2), gamma(3) of the ring R = F-p [u]/< u(k+1) - u >, with gamma(1)+ gamma(2) + gamma(3) = 1, R is decomposed as R = gamma R...
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Let p be an odd prime, and k be an integer such that gcd(k,p) = 1. Using pairwise orthogonal idempotents gamma(1), gamma(2), gamma(3) of the ring R = F-p [u]/< u(k+1) - u >, with gamma(1)+ gamma(2) + gamma(3) = 1, R is decomposed as R = gamma R-1 circle plus gamma R-2 circle plus gamma R-3, which contains the ring R = gamma F-1(p) circle plus gamma F-2(p) circle plus gamma F-3(p) as a subring. It is shown that, for lambda(0), lambda(k) is an element of F-p, lambda(0) + u(k)lambda(k) is an element of R, and it is invertible if and only if lambda(0) and lambda(0) + lambda(k) are units of F-p. In such cases, we study (lambda(0) + u(k)lambda(k))-constacyclic codes over R. We present a direct sum decomposition of (lambda(0) + u(k)lambda(k))-constacyclic codes and their duals, which provides their corresponding generators. Necessary and sufficient conditions for a (lambda(0) + u(k)lambda(k))-constacyclic code to contain its dual are obtained. As an application, many new quantum codes over F-p, with better parameters than existing ones, are constructed from cyclic and negacyclic codes over R.
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A comprehensive performance analysis of sinusoidal and code excited linear prediction (CELP) speech coding is given around 4 kbit/s, using both subjective and objective measurements. Based on the observations made, justification f...
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A comprehensive performance analysis of sinusoidal and code excited linear prediction (CELP) speech coding is given around 4 kbit/s, using both subjective and objective measurements. Based on the observations made, justification for the multi-modal hybrid coding approach employing both sinusoidal and CELP coding is given, and an implementation of such a coder is described. This 4 kbit/s sinusoidal/CELP speech coder utilizes four modes to classify the input speech segment: voiced, jittery-voiced, plosive and unvoiced. For voiced segments sinusoidal coding is used whereas different CELP versions are employed for the other modes. The quality of the implemented 4 kbit/s sinusoidal/ CELP speech coder in clean speech conditions is finally verified by a listening test. In the test, the 4 kbit/s coder performed almost as well as-the high-quality references used, but it still needs improvements to be classified as a high-quality 4 kbit/s speech coder.
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As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and...
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As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and 3-generator QC codes are studied, and many good, new QC codes are constructed from simplex codes. Some new binary QC codes or related codes, that improve the bounds on maximum minimum distance for binary linear codes are constructed. They are 5-generator QC [93,17,34] and [254,23,102] codes, and related [96,17,36], [256,23,104] codes
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