期刊名称：IAENG International Journal of Computer Science
印刷版ISSN：1819-656X
电子版ISSN：1819-9224
出版年度：2021
卷号：48
期号：3
语种：English
出版社：IAENG - International Association of Engineers
摘要：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. The Lee weight and the Gray map for these codes are defined and MacWilliams relations for complete, symmetrized, and Lee weight enumerators are derived. The Singleton bound as well as maximum distance separable codes are also considered. Furthermore, cyclic and quasi-cyclic codes are discussed, and as an application some new linear codes over Z4 with the highest known minimum Lee distance are also obtained.
