非交换环上的循环码

2017 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO) Pub Date : 2017-04-01 DOI:10.1109/ICMSAO.2017.7934873

S. Akbiyik, B. A. Ersoy

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引用次数: 0

摘要

系数来自于3的四元数环是一个非交换有限环。给出了H3 = 0 3 + 0 3i + 0 3j + 0 3k上的线性码和循环码的结构。同时，给出了环上线性码的标准生成矩阵。证明了H3分解为两部分，即具有幂等系数的s3 + s3i。注意这两个部分是可交换的。给出了环上是循环码的充分必要条件。在此基础上，给出了循环码的生成多项式，并得到了循环码的参数。

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Cyclic codes over a non-commutative ring

Quaternion ring with coefficient from ℤ3 is a non-commutative finite ring. The structure of linear and cyclic codes over H3 = ℤ3 + ℤ3i + ℤ3j + ℤ3k is given. Also, a generator matrix in standard form for linear codes over the ring is given. It is shown that H3 decomposes into two parts form ℤ3+ℤ3i with idempotent coefficients. Notice that the parts are commutative. We give the necessary and sufficient condition of being a cyclic code over the ring. Further, we give a generator polynomial for a cyclic code and get parameters of it.

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2017 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO)

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