Results 191 to 200 of about 59,107 (223)
Some of the next articles are maybe not open access.
Optimal ternary quasi-cyclic codes
Designs, Codes and Cryptography, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Phil P. Greenough, Ray Hill
openaire +2 more sources
IEEE Communications Letters, 2018
Low-density parity-check (LDPC) codes based on affine permutation matrices, APM-LDPC codes, have been attracted recently, because of some advantages rather than QC-LDPC codes in minimum-distance, cycle distribution and error-rate performance. In this letter, circulant and anti-circulant permutation matrices are used to define a class of LDPC codes ...
Zahra Gholami, Mohammad Gholami
openaire +1 more source
Low-density parity-check (LDPC) codes based on affine permutation matrices, APM-LDPC codes, have been attracted recently, because of some advantages rather than QC-LDPC codes in minimum-distance, cycle distribution and error-rate performance. In this letter, circulant and anti-circulant permutation matrices are used to define a class of LDPC codes ...
Zahra Gholami, Mohammad Gholami
openaire +1 more source
A SPECIAL CLASS OF QUASI-CYCLIC CODES
Bulletin of the Australian Mathematical Society, 2017We study a special class of quasi-cyclic codes, obtained from a cyclic code over an extension field of the alphabet field by taking its image on a basis. When the basis is equal to its dual, the dual code admits the same construction. We give some examples of self-dual codes and LCD codes obtained in this way.
Shi, Minjia +4 more
openaire +1 more source
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
openaire +2 more sources
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
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.
openaire +1 more source
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.
openaire +1 more source
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
openaire +2 more sources