On the codes over the ring
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In this paper, we construct the ring M2 = F2 + u1F2 + u2F2 + u1u2F2, where u21 = 1,u22 = 1, u1u2 = u2u1. Firstly, we investigate the structure of the ring. Then we describe two Gray maps which are shown to be equivalent and it is obtained that C is the Gray image of a linear code over M2 if and only if C is invariant under the permutation group K4 = {1, , , }. Morever we investigate Euclidean self dual codes over M2.
Abstract
In this paper, we construct the ring M2 = F2 + u1F2 + u2F2 + u1u2F2, where u21 = 1,u22 = 1, u1u2 = u2u1. Firstly, we investigate the structure of the ring. Then we describe two Gray maps which are shown to be equivalent and it is obtained that C is the Gray image of a linear code over M2 if and only if C is invariant under the permutation group K4 = {1, , , }. Morever we investigate Euclidean self dual codes over M2.
참고문헌 (4)
- S.T.Dougherty, "Gray maps and Their bi- nary Images", Finite Fields and Their Applications, 17(3), pp.205~219 (2011)
- S.T.Dougherty, "Self dual codes over Rk and binary self dual codes"
- I.Siap, "Linear codes over F2+uF2 and their complete weight enumerators", OSU Dijen Conference, Codes and Designs (2002), Ohio State Univ
- B. Yildiz, "Linear codes over F2 + u1F2 + u2F2 + u1u2F2", Des. Codes Cryptogr, 54(1), pp.61~81 (2010)