On extendability of additive code isometries

Serhii  Dyshko

doi:10.3934/amc.2016.10.45

Article Contents

2016, Volume 10, Issue 1: 45-52. Doi: 10.3934/amc.2016.10.45

This issue Previous Article Convolutional codes with a matrix-algebra word-ambient Next Article Yet another variation on minimal linear codes

On extendability of additive code isometries

Serhii Dyshko^1,

1.
IMATH, Université de Toulon, B.P. 20132, 83957 La Garde

Received: November 2014

Revised: July 2015

Published: February 2016

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Abstract

For linear codes, the MacWilliams Extension Theorem states that each linear isometry of a linear code extends to a linear isometry of the whole space. But, in general, this is not the situation for nonlinear codes. In this paper codes over a vector space alphabet are considered. It is proved that if the length of such code is less than some threshold value, then an analogue of the MacWilliams Extension Theorem holds. One family of unextendable code isometries for the threshold value of code length is described.

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Mathematics Subject Classification: Primary: 94B05; Secondary: 05B40.

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