Hermitian dual containing BCH codes and Construction of new quantum codes (pp0021-0035)
          Ruihu Li, Fei Zou, Yang Liu, and Zongben Xu
          doi: https://doi.org/10.26421/QIC13.1-2-3
Abstracts: Let q ≥ 3 be a prime power. Maximal designed distances of primitive Hermitian dual containing q 2 -ary BCH codes (narrow-sense or non-narrow-sense) are determined by a careful analysis of properties of cyclotomic cosets. Non-narrow-sense BCH codes which achieve these maximal designed distances are presented, and a sequence of nested nonnarrow-sense BCH codes that contain these BCH codes with maximal designed distances are constructed and their parameters are computed. Consequently, new nonbinary quantum BCH codes are derived from these non-narrow-sense BCH codes. The nonbinary quantum BCH codes presented here have better parameters than those quantum BCH codes available in the literature.
Key words:  cyclotomic cosets, BCH (Bose-Chaudhuri-Hocquenghem) codes, dual codes, dimension, quantum codes