Some constructions of linearly optimal group codes

  • Couselo E
  • González S
  • Markov V
 et al. 
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Abstract

We continue here the research on (quasi)group codes over (quasi)group rings. We give some constructions of [n, n - 3, 3]q-codes over Fqfor n = 2 q and n = 3 q. 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 FqG where G is an elementary abelian group of order q. © 2010 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • Group code
  • Group ring
  • Linearly optimal code
  • Reed-Solomon code

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