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On Counting Subring-Subcodes of Free Linear Codes Over Finite Principal Ideal Rings (1612.02213v1)
Published 7 Dec 2016 in cs.IT and math.IT
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 $k_0 = rank_R (B\cap Rl)$. This corrects a wrong result which was given in the case of finite fields.