Z_pZ_p[u]-Additive Cyclic Code And Their Applications

In this paper,the algebraic structures of Z_pZ_p[u]-additive cyclic codes and one-Lee weight and two-Lee weight Z₂Z₂[u]-additive are studied.The details are given as follows:（1）Additive cyclic codes over Z_pZ_p[u]are discussed,the relationship between（1-u）-additive constacyclic code and additive cyclic code is studied.A new Gray map from Z_pZ_p[u]to Z_P^α+Pβ is defined,it is proved that the Gray image of a（1-u）-additive constacyclic code C is a generalized quasi-cyclic code.Additionally,the structure of Z_pZ_p[u]-additive cyclic codes is obtained and their minimal spanning sets are also given.（2）One-Lee weight and two-Lee weight codes over Z₂Z₂[u]are studied.Some properties of one-Lee weight Z₂Z₂[u]-additive codes are given,and a complete classification of one-Lee weight Z₂Z₂[u]-additive formally self-dual codes is obtained.The structure of two-Lee weight projective Z₂Z₂[u]codes is determined.Some optimal binary linear codes are obtained directly from one-Lee weight and two-Lee weight Z_pZ_p[u]-additive codes via the extended Gray map.