Some Classes of Mixed Alphabet Codes With Few Weights

Abstract

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 $\mathbb {F}_{p}R$ -additive codes, where $p$ is a prime number, and ${R}= \mathbb {F}_{{p}}+{u} \mathbb {F}_{{p}}$ with $u^{2}=0$ . These codes can be viewed as a combination of irreducible cyclic codes over $\mathbb {F}_{{p}}$ and 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.