American Institute of Mathematical Sciences

February  2016, 10(1): 45-52. doi: 10.3934/amc.2016.10.45

On extendability of additive code isometries

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

Received  November 2014 Revised  July 2015 Published  March 2016

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.
Citation: Serhii Dyshko. On extendability of additive code isometries. Advances in Mathematics of Communications, 2016, 10 (1) : 45-52. doi: 10.3934/amc.2016.10.45
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