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In this paper, by analyzing the solutions of certain equations over , we present four classes of optimal ternary cyclic codes with parameters . It is shown that some recent work on this class of optimal ternary cyclic codes are special cases of our results. 相似文献
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Cyclic code is an interesting topic in coding theory and communication systems. In this paper, we investigate the ternary cyclic codes with parameters based on some results proposed by Ding and Helleseth in 2013. Six new classes of optimal ternary cyclic codes are presented by determining the solutions of certain equations over . 相似文献
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A cyclic code is a -ary cyclic code of length , minimum Hamming distance and weight . In this paper, we investigate cyclic codes. A new upper bound on , the largest possible number of codewords in a cyclic code, is given. Two new constructions for optimal cyclic codes based on cyclic difference packings are presented. As a consequence, the exact value of is determined for any positive integer . We also obtain some other infinite classes of optimal cyclic codes. 相似文献
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《Discrete Mathematics》2019,342(11):3098-3113
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The locality of locally repairable codes (LRCs) for a distributed storage system is the number of nodes that participate in the repair of failed nodes, which characterizes the repair cost. In this paper, we first determine the locality of MacDonald codes, then propose three constructions of LRCs with . Based on these results, for and , we give an optimal linear code with small locality. The distance optimality of these linear codes can be judged by the codetable of M. Grassl for and by the Griesmer bound for . Almost all the codes () have locality except for the three codes, and most of the code with achieves the Cadambe–Mazumdar bound for LRCs. 相似文献
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