Hulls of cyclic and negacyclic codes over finite fields

Hulls of cyclic and negacyclic codes over finite fields

We study the hulls of cyclic and negacyclic codes of length n over a finite field Fq with respect to the Euclidean and Hermitian inner products. Based on the characterization of their generator polynomials, the dimensions of the hulls of cyclic and negacyclic codes of length n over Fq are determined...

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Bibliographic Details
Main Authors: Sangwisut, Ekkasit, Jitman, Somphong, Ling, San, Udomkavanich, Patanee
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2015
Subjects:
DRNTU::Science::Mathematics::Discrete mathematics::Algorithms
Online Access:https://hdl.handle.net/10356/107296
http://hdl.handle.net/10220/25441
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Institution: Nanyang Technological University
Language: English
Description
Summary:We study the hulls of cyclic and negacyclic codes of length n over a finite field Fq with respect to the Euclidean and Hermitian inner products. Based on the characterization of their generator polynomials, the dimensions of the hulls of cyclic and negacyclic codes of length n over Fq are determined. The enumerations of cyclic codes and negacyclic codes of length n over Fq having hulls of a given dimension are established as well. As special cases, known results concerning complementary dual and self-dual cyclic codes can be viewed as corollaries of the results in this paper.

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