A class of constacyclic BCH codes

  • Zhonghua Sun
  • Shixin Zhu
  • Liqi WangEmail author


Constacyclic codes are a subclass of linear codes and have been well studied. Constacyclic BCH codes are a family of constacyclic codes and contain BCH codes as a subclass. Compared with the in-depth study of BCH codes, there are relatively little study on constacyclic BCH codes. The objective of this paper is to determine the dimension and minimum distance of a class of q-ary constacyclic BCH codes of length \(\frac {q^{m}-1}{q-1}\) with designed distances \(\delta _{i}=q^{m-1}-\frac {q^{\lfloor \frac {m-3}2 \rfloor +i }-1}{q-1}\) for \(1\leq i\leq \min \limits \{\lceil \frac {m+1}2 \rceil -\lfloor \frac {m}{q+1} \rfloor , \lceil \frac {m-1}2 \rceil \}\). As will be seen, some of these codes are optimal.


Constacyclic code BCH code Minimum distance 

Mathematics Subject Classification (2010)

94B05 94B15 



The authors are grateful to the anonymous reviewers for careful reading and for valuable suggestions. Thank the reviewer for generously sharing the Magma programs with us so that we can check the correctness of the results in the text.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsHefei University of TechnologyHefeiChina

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