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Erschienen in:
24.11.2020 | Original Research
\({\pmb {{\mathbb {Z}}}}_p{\pmb {{\mathbb {Z}}}}_p[v]\)-additive cyclic codes are asymptotically good
Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2021
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Abstract
We construct a class of \({\mathbb {Z}}_p{\mathbb {Z}}_p[v]\)-additive cyclic codes, where p is a prime number and \(v^2=v\). We determine the asymptotic properties of the relative minimum distance and rate of this class of codes. We prove that, for any positive real number \(0<\delta <1\) such that the p-ary entropy at \(\frac{k+l}{2}\delta \) is less than \(\frac{1}{2}\), the relative minimum distance of the random code is convergent to \(\delta \) and the rate of the random code is convergent to \(\frac{1}{k+l}\), where p, k, l are pairwise coprime positive integers.