Results 221 to 230 of about 22,216 (258)
Some of the next articles are maybe not open access.
Binary Quasi-Cyclic Goppa Codes
Designs, Codes and Cryptography, 2000A class of quasi-cycic Goppa codes containing irreducibles codes, and partially split ones, is defined. A necessary and sufficient condition for a Goppa code to be quasi-cyclic is given. One more sufficient condition is derived on the defining polynomial of the Goppa code.
Bommier, Grégoire, Blanchet, Francis
openaire +1 more source
Applied Mathematics-A Journal of Chinese Universities, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pei, Junying, Zhang, Xuejun
openaire +2 more sources
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pei, Junying, Zhang, Xuejun
openaire +2 more sources
Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252), 2002
Many binary quasi-cyclic codes have a better minimum distance than other known linear codes with the same parameters. We present 43 new quasi-cyclic codes, which improve on the parameters of previously found quasi-cyclic codes. Five of them even improve the lower bound on the minimum distance for linear codes.
P. Heijnen, H. van Tilborg, S. Weijs
openaire +1 more source
Many binary quasi-cyclic codes have a better minimum distance than other known linear codes with the same parameters. We present 43 new quasi-cyclic codes, which improve on the parameters of previously found quasi-cyclic codes. Five of them even improve the lower bound on the minimum distance for linear codes.
P. Heijnen, H. van Tilborg, S. Weijs
openaire +1 more source
Optimal ternary quasi-cyclic codes
Designs, Codes and Cryptography, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Greenough, P. P., Hill, Raymond
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
Paracyclic and quasi-cyclic groups
Annali di Matematica Pura ed Applicata, 1986Let G be a finite group. The authors define the multiplicity \(\gamma_ G\) of G to be the maximum of \(| (x\in G:\) \(x^ d=1)| /d\) taken over all divisors d of \(| G|\), and the cocyclicity \(\iota_ G\) as the least index in G of any cyclic subgroup of G. In earlier work [\textit{R. Dvornicich} and \textit{M. Forti}, J.
DVORNICICH, ROBERTO, FORTI, MARCO
openaire +2 more sources
Quasi-cyclic binary Goppa codes
Proceedings of IEEE International Symposium on Information Theory, 2002We give here a necessary and sufficient condition for a binary Goppa code to be quasi-cyclic, a sufficient condition easier to check, a partial converse and some specific forms for quasi-cyclic Goppa codes.
F. Blanchet, G. Bommier
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
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 ...
Townsend, Richard L. +1 more
openaire +2 more sources
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