On the Gray images of some constacyclic codes over Fp+ u Fp+ u2Fp

作者：Yu Haifeng^*; Zhu Shixin; Kai Xiaoshan

来源：Journal of Systems Science and Complexity, 2016, 29(3).

DOI：10.1007/s11424-015-4316-5

• Coding Theory
• Constacyclic codes
• Cyclic code
• Gray map
• Linear codes
• Linear cyclic code
• Optimal linear code
• Repeated-root cyclic codes

Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, a new Gray map between codes over Fp+ uFp+ u2Fpand codes over Fpis defined, where p is an odd prime. By means of this map, it is shown that the Gray image of a linear (1+u+u2)-constacyclic code over Fp+ uFp+ u2Fpof length n is a repeated-root cyclic code over Fpof length pn. Furthermore, some examples of optimal linear cyclic codes over F3from (1 + u + u2)-constacyclic codes over F3 + uF3+ u2F3are given.

• 单位
  合肥工业大学; 东南大学