Group codes over fields are asymptotically good

04/24/2019

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by   Martino Borello, et al.

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Group codes are right or left ideals in a group algebra of a finite group over a finite field. Following ideas of Bazzi and Mitter on group codes over the binary field, we prove that group codes over finite fields of any characteristic are asymptotically good. On the way we extend a result of Massey on the fractional weight of distinct binary n-tuples and a result of Piret on an upper bound on the weight distribution of a binary code to any finite field.