Constructing MDS Galois self-dual constacyclic codes over finite fields
Constructing MDS Galois self-dual constacyclic codes over finite fields
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DOI：
10.1016/j.disc.2021.112388
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Jiafu Mi;X. Cao
中科院分区：
文献类型：
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作者：
Jiafu Mi;X. Cao
作为论文中两个例子（Fan and Zhang, 2017）的进一步发展和深化，我们在有限域上构造了MDS伽罗瓦自对偶常环码。首先给出了正态MDS常环码的定义，并探讨了其存在条件。进一步给出了正常MDS伽罗瓦自对偶常环码的存在条件。基于后一个条件，我们对F q上长度为n的所有正规MDS伽罗瓦自对偶λ-常环码进行了分类和构造，其中q= p e是奇素数幂，gcd (q, n)= 1, λ∈F q∗。
As a further development and deepening of two examples in the paper (Fan and Zhang, 2017), we construct MDS Galois self-dual constacyclic codes over finite fields. First, we give the definition of normal MDS constacyclic codes and explore their existence conditions. Further, we give existence conditions for normal MDS Galois self-dual constacyclic codes. Based on the latter conditions, we classify and construct all normal MDS Galois self-dual λ-constacyclic codes over F q of length n, where q= p e is an odd prime power, gcd (q, n)= 1 and λ∈ F q∗.