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Keywords = negacyclic codes

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11 pages, 303 KiB  
Article
Quantum Codes from Constacyclic Codes over the Ring Fq[u1,u2]/〈 u 1 2 -u1, u 2 2 -u2,u1u2-u2u1
by Ahmad N. Alkenani, Mohammad Ashraf and Ghulam Mohammad
Mathematics 2020, 8(5), 781; https://doi.org/10.3390/math8050781 - 13 May 2020
Cited by 6 | Viewed by 2664
Abstract
In this paper, we study the structural properties of ( α + u 1 β + u 2 γ + u 1 u 2 δ ) -constacyclic codes over [...] Read more.
In this paper, we study the structural properties of ( α + u 1 β + u 2 γ + u 1 u 2 δ ) -constacyclic codes over R = F q [ u 1 , u 2 ] / u 1 2 u 1 , u 2 2 u 2 , u 1 u 2 u 2 u 1 where q = p m for odd prime p and m 1 . We derive the generators of constacyclic and dual constacyclic codes. We have shown that Gray image of a constacyclic code of length n is a quasi constacyclic code of length 4 n . Also we have classified all possible self dual linear codes over this ring R . We have given the applications by computing non-binary quantum codes over this ring R . Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
10 pages, 285 KiB  
Article
The Average Hull Dimension of Negacyclic Codes over Finite Fields
by Somphong Jitman and Ekkasit Sangwisut
Math. Comput. Appl. 2018, 23(3), 41; https://doi.org/10.3390/mca23030041 - 20 Aug 2018
Cited by 5 | Viewed by 2710
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 [...] Read more.
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. Full article
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