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Math. Comput. Appl. 2018, 23(3), 41; https://doi.org/10.3390/mca23030041

The Average Hull Dimension of Negacyclic Codes over Finite Fields

1
Department of Mathematics, Faculty of Science, Silpakorn University, Nakhon Pathom 73000, Thailand
2
Department of Mathematics and Statistics, Faculty of Science, Thaksin University, Phattalung 93110, Thailand
*
Author to whom correspondence should be addressed.
Received: 6 August 2018 / Revised: 17 August 2018 / Accepted: 17 August 2018 / Published: 20 August 2018
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Abstract

Hulls of linear codes have been extensively studied due to their wide applications and links with the efficiency of some algorithms in coding theory. In this paper, the average dimension of the Euclidean hull of negacyclic codes of length n over finite fields F q , denoted by E ( n , 1 , q ) , has been investigated. The formula for E ( n , 1 , q ) has been determined. Some upper and lower bounds of E ( n , 1 , q ) have been given as well. Asymptotically, it has been shown that either E ( n , 1 , q ) is zero or it grows the same rate as n. View Full-Text
Keywords: average hull dimension; negacyclic codes; hulls; self-reciprocal polynomials average hull dimension; negacyclic codes; hulls; self-reciprocal polynomials
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Jitman, S.; Sangwisut, E. The Average Hull Dimension of Negacyclic Codes over Finite Fields. Math. Comput. Appl. 2018, 23, 41.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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