2016/01/18 by Ping Li, Li, Ping, Xuemei Guo +3
Computer Science · Mathematics · #Coding theory and cryptography #Finite Group Theory Research #Cooperative Communication and Network Coding
paper · pdf · doi:10.48550/arxiv.1601.04453
In this paper, we mainly study the theory of linear codes over the ring R =ℤ4+uℤ4+vℤ4+uvℤ4. By the Chinese Remainder Theorem, we have R is isomorphic to the direct sum of four rings ℤ4. We define a Gray map Φ from Rn to ℤ44n, which is a distance preserving map. The Gray image of a cyclic code over Rn is a linear code over ℤ4. Furthermore, we study the MacWilliams identities of linear codes over R and give the the generator polynomials of cyclic codes over R. Finally, we discuss some properties of MDS codes over R.