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arXiv · 1612.02213

On Counting Subring-Subcodes of Free Linear Codes Over Finite Principal Ideal Rings

Ramakrishna Bandi·Alexandre Fotue Tabue·Edgar Martínez-Moro
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Abstract

Let $R$ be a finite principal ideal ring and $S$ the Galois extension of $R$ of degree $m$. For $k$ and $k_0$, positive integers we determine the number of free $S$-linear codes $B$ of length $l$ with the property $k = rank_S(B)$ and $k_0 = rank_R (B\cap R^l)$. This corrects a wrong result which was given in the case of finite fields.

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Ramakrishna Bandi, Alexandre Fotue Tabue, Edgar Martínez-Moro. 2016-12-07. On Counting Subring-Subcodes of Free Linear Codes Over Finite Principal Ideal Rings. https://arxiv.org/abs/1612.02213

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