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.
Couselo, E., González, S., Markov, V., Martínez, C., & Nechaev, A. (2010). Some constructions of linearly optimal group codes. Linear Algebra and Its Applications, 433(2), 356–364. https://doi.org/10.1016/j.laa.2010.03.002