On the weight distribution of codes over finite rings

Eimear Byrne

doi:10.3934/amc.2011.5.395

Article Contents

2011, Volume 5, Issue 2: 395-406. Doi: 10.3934/amc.2011.5.395

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On the weight distribution of codes over finite rings

Eimear Byrne^1,

1.
School of Mathematical Sciences, University College Dublin, Springfield, MO 65801-2604

Received: April 30, 2010

Revised: October 31, 2010

Published: April 2011

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Abstract

Let $R>S$ be finite Frobenius rings for which there exists a trace map $T:$ _S$R \rightarrow$_S$R$. Let $C$_f,s$:=\{x \mapsto T(\alpha x + \beta f(x)) : \alpha, \beta \in R \}$. $C$_f,s is an $S$-linear subring-subcode of a left linear code over $R$. We consider functions $f$ for which the homogeneous weight distribution of $C$_f,s can be computed. In particular, we give constructions of codes over integer modular rings and commutative local Frobenius that have small spectra.

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Mathematics Subject Classification: Primary: 11T71; Secondary: 14G50.

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