Abstract
In this paper, we study a special class of \({\mathbb {Z}}_p{\mathbb {Z}}_p[u]\)-additive code \(C_L\) defined in terms of the down-set, where \(u^2=u\) and p is an odd prime. By a proper choice of the down-set, we determine the weight distribution of the additive code \(C_L\). In particular, we obtain several infinite families of minimal and optimal few-weight p-codes via the Gray map, and these codes can be applied to secret sharing schemes.
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The work of M. Shi is supported by the National Natural Science Foundation of China (12071001), the Excellent Youth Foundation of Natural Science Foundation of Anhui Province (1808085J20).
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Wang, S., Shi, M. Few-weight \({\pmb {{\mathbb {Z}}}}_p\pmb {{\mathbb {Z}}}_p[u]\)-additive codes from down-sets. J. Appl. Math. Comput. 68, 2381–2388 (2022). https://doi.org/10.1007/s12190-021-01594-x
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DOI: https://doi.org/10.1007/s12190-021-01594-x