Abstract
A cyclic \((n,d,w)_q\) code is a cyclic q-ary code of length n, constant-weight w and minimum distance d. A cyclic \((n,d,w)_q\) code with the largest possible number of codewords is said to be optimal. Optimal nonbinary cyclic \((n,d,w)_q\) codes were first studied in our recent paper (Lan et al. in IEEE Trans Inf Theory 62(11):6328–6341, 2016). In this paper, we continue to discuss the constructions of optimal cyclic \((n,4,3)_q\) codes. We establish the connection between cyclic \((n,4,3)_{q}\) codes and \(q-1\) mutually orbit-disjoint cyclic (n, 3, 1) difference packings (briefly (n, 3, 1)-CDPs). For the case of \(q=4\), we construct three mutually orbit-disjoint (n, 3, 1)-CDPs by constructing a pair of strongly orbit-disjoint (n, 3, 1)-CDPs, which are obtained from Skolem-type sequences. As a consequence, we completely determine the number of codewords of an optimal cyclic \((n,4,3)_{4}\) code.
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Supported by the NSFC under Grant 11431003 (Y. Chang), and the NSFC under Grant 11401582 and the NSFHB under Grant A2015507019 (L. Wang).
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Lan, L., Chang, Y. & Wang, L. Constructions of cyclic quaternary constant-weight codes of weight three and distance four. Des. Codes Cryptogr. 86, 1063–1083 (2018). https://doi.org/10.1007/s10623-017-0379-8
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DOI: https://doi.org/10.1007/s10623-017-0379-8