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Self-orthogonal quasi-cyclic codes
IEEE Transactions on Information Theory, 1967A new class of linear block codes, called self-orthogonal quasi-cyclic codes, is defined. It is shown that the problem of designing these codes is equivalent to the problem of designing disjoint difference sets. As a result, several classes of optimal and near-optimal codes can be constructed analytically and other codes can be found by a computer ...
Richard L. Townsend +1 more
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On spectral design methods for quasi-cyclic codes
2016 IEEE International Symposium on Information Theory (ISIT), 2016A method is provided for constructing upper triangular square matrices over the univariate polynomial ring over a finite field, under certain constraints on the eigenvalues of the matrices. In some cases of interest, the degree of the determinant of such matrices is shown to be the smallest possible.
Ron M. Roth, Alexander Zeh
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On the Girth of Quasi-Cyclic Protograph LDPC Codes
IEEE Transactions on Information Theory, 2012In this paper, we study the relationships between the girth of the Tanner graph of a quasi cyclic (QC) protograph low-density parity-check (LDPC) code, on one hand, and the lifting degree and the size and the structure of the base graph, on the other hand.
Mehdi Karimi, Amir H. Banihashemi
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Projective spaces and quasi-cyclic codes
Ars Comb., 1998The incidence matrix of a finite projective plane of order \(q\) can be arranged as a circulant matrix with ones on the diagonal. By appending a unit matrix one obtains a generating matrix for a binary code that is studied in the paper. It is a double circulant \([2(q^2 + q +1), q^2+ q + 1, q+2]\)-code, and, if \(q\) is odd, by omitting the odd-weight ...
T. Aaron Gulliver, Vijay K. Bhargava
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New codes from chains of quasi-cyclic codes
Proceedings. International Symposium on Information Theory, 2005. ISIT 2005., 2005Well known constructions are applied to chains of quasi-cyclic codes in order to achieve new codes that improve on best known bounds on the minimum distance. These techniques have previously been successfully applied to chains of cyclic and algebraic-geometric codes.
Markus Grassl, Greg White 0001
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2014
In this chapter, we recall the main definitions concerning quasi-cyclic codes, which will be used in the remainder of the book. We introduce the class of circulant matrices, and the special class of circulant permutation matrices, together with their isomorphism with polynomials over finite fields.
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In this chapter, we recall the main definitions concerning quasi-cyclic codes, which will be used in the remainder of the book. We introduce the class of circulant matrices, and the special class of circulant permutation matrices, together with their isomorphism with polynomials over finite fields.
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A link between quasi-cyclic codes and convolutional codes
IEEE Transactions on Information Theory, 1998Summary: Given a quasi-cyclic code with minimum Hamming distance \(d\), a set of convolutional codes is derived with free distance equal to \(d\). It is shown that an increase in the rate of these codes results in a decrease in the memory length. The connection between these codes is illustrated with several well-known quasi-cyclic codes.
Morteza Esmaeili +3 more
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The structure of generalized quasi cyclic codes
2005The structure of generalized quasi-cyclic (GQC) codes is investigated. These are codes in which a permutation automorphism has orbits of varying lengths on the coordinate positions. A BCH-type bound is derived which is similar to that for quasi-cyclic (QC) codes.
ŞİAP, İrfan, Kulhan, Nilgün
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On generalizations of skew quasi-cyclic codes
2020Summary: In the last two decades, codes over noncommutative rings have been one of the main trends in coding theory. Due to the fact that noncommutativity brings many challenging problems in its nature, still there are many open problems to be addressed.
BEDİR, Sümeyra +2 more
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On the duals of quasi-cyclic codes and their application to quantum codes
Quantum Information ProcessingzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shivanshu Benjwal, Maheshanand Bhaintwal
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