2019/04/25 by Bustomi, Aditya Purwa Santika, Santika, Aditya Purwa +2
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1904.11117
openalex publication_date 2019/04/25 · openalex created_date 2019/05/03 · openalex updated_date 2026/07/28
We investigate linear codes over the ring ℤ4 + uℤ4 + vℤ4 + wℤ4 + uvℤ4 + uwℤ4 + vwℤ4 + uvwℤ4, with conditions u2=u, v2=v, w2=w, uv=vu, uw=wu and vw=wv. We first analyze the structure of the ring and then define linear codes over this ring. Lee weight and Gray map for these codes are defined and MacWilliams relations for complete, symmetrized, and Lee weight enumerators are obtained. The Singleton bound as well as maximum distance separable codes are also considered. Furthermore, cyclic and quasi-cyclic codes are discussed, and some examples are also provided.