1. The maximum designed distances of dual-containing non-primitive BCH codes.
- Author
-
Li, Fengwei, Yue, Qin, and Huang, Daitao
- Subjects
- *
LINEAR codes , *INTEGERS - Abstract
Let q be a prime power and m a positive integer. Suppose that a ≥ 2 is a factor of q m − 1 such that m is the multiplicative order of q modulo n : = q m − 1 a. Firstly, for m odd and m even, we present some necessary and sufficient conditions on dual-containing non-primitive BCH codes of length n with the maximum designed distances over F q , respectively. The results show that the maximum designed distances of dual-containing BCH codes in this paper are larger than those in [2, Theorem 3]. Secondly, we explicitly determine the dimensions of some dual-containing non-primitive BCH codes of length n , and finally, we construct some new quantum codes with relatively large minimum distances. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF