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Some constructions of linearly optimal group codes

✍ Scribed by Elena Couselo; Santos González; Victor Markov; Consuelo Martínez; Alexander Nechaev

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
162 KB
Volume
433
Category
Article
ISSN
0024-3795

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✦ Synopsis

We continue here the research on (quasi)group codes over (quasi)group rings. We give some constructions of [n, n -3, 3] qcodes over F q for n = 2q and n = 3q. These codes are linearly optimal, i.e. have maximal dimension among linear codes having a given length and distance. Although codes with such parameters are known, our main results state that we can construct such codes as (left) group codes. In the paper we use a construction of Reed-Solomon codes as ideals of the group ring F q G where G is an elementary abelian group of order q.

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