Some Classes of Mixed Alphabet Codes With Few Weights
Rongsheng Wu, Minjia Shi · IEEE Communications Letters · 2020
Mixed alphabet codes are the generalizations of the classical linear codes over finite fields and rings. In this letter we introduce a valid method of constructing \mathbb FpR-additive codes, where p is a prime number, and R = \mathbb Fp+u \mathbb Fpwith u2=0. These codes can be viewed as a combination of irreducible cyclic codes over \mathbb Fpand trace codes over R. In particular, by using the Gray map, part of the obtained image codes meets the Greismer bound with equality, and can be applied to construct new secret sharing scheme.