Results 11 to 20 of about 1,655,518 (300)
Quasi-cyclic subcodes of cyclic codes [PDF]
SIAM Journal on Discrete Mathematics, 2016 We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration is equivalent
Belfiore, Jean-Claude +2 more
core +8 more sources
Quasi-Cyclic Constructions of Quantum Codes [PDF]
Finite Fields and Their Applications, 2017 We give sufficient conditions for self-orthogonality with respect to symplectic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index two. We provide lower bounds for the symplectic weight and the minimum distance of the
C. Galindo +2 more
semanticscholar +5 more sources
Structure and performance of generalized quasi-cyclic codes [PDF]
Finite Fields and Their Applications, 2017 Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets.
Cem Güneri +5 more
semanticscholar +6 more sources
Spectral Analysis of Quasi-Cyclic Product Codes [PDF]
IEEE Transactions on Information Theory, 2015 This paper considers a linear quasi-cyclic product code of two given quasi-cyclic codes of relatively prime lengths over finite fields. We give the spectral analysis of a quasi-cyclic product code in terms of the spectral analysis of the row and column ...
Alexander Zeh, S. Ling
semanticscholar +4 more sources
Construction of Quasi-Cyclic Product Codes
CoRR, 2015 Linear quasi-cyclic product codes over finite fields are investigated. Given the generating set in the form of a reduced Gr{\"o}bner basis of a quasi-cyclic component code and the generator polynomial of a second cyclic component code, an explicit ...
Ling, San, Zeh, Alexander
core +2 more sources
Quasi-Cyclic Asymptotically Regular LDPC Codes [PDF]
2010 IEEE Information Theory Workshop, 2010 Families of "asymptotically regular" LDPC block code ensembles can be formed by terminating (J,K)-regular protograph-based LDPC convolutional codes. By varying the termination length, we obtain a large selection of LDPC block code ensembles with varying ...
Costello Jr, Daniel J. +3 more
core +2 more sources
Multidimensional Quasi-Cyclic and Convolutional Codes [PDF]
IEEE Transactions on Information Theory, 2016 We introduce multidimensional analogues of quasi-cyclic (QC) codes and study their algebraic structure. We demonstrate a concatenated structure for multidimensional QC codes and use this to prove that this class of codes is asymptotically good. We also relate the new family of codes to convolutional codes.
Cem Güneri, Buket Özkaya
semanticscholar +5 more sources
Existence and Uniqueness of Fixed Point for Cyclic Mappings in Quasi-αb-Metric Spaces
InPrime, 2022 The fixed point theory remains the most important and preferred topic studied in mathematical analysis. This study discusses sufficient conditions to prove a unique fixed point in quasi-αb-metric spaces with cyclic mapping. The analysis starts by showing
Ainun Sukmawati Al Idrus +4 more
doaj +1 more source
IEEE Transactions on Communications, 2021 In his pioneering work on LDPC codes, Gallager dismissed codes with parity-check matrices of weight two after proving that their minimum Hamming distances grow at most logarithmically with their code lengths.
Xin Xiao +4 more
semanticscholar +1 more source
An integer programming model for obtaining cyclic quasi-difference matrices
Operations Research Perspectives, 2023 Orthogonal arrays are of great importance in mathematical sciences. This paper analyses a certain practical advantage of quasi-difference matrices over difference matrices to obtain orthogonal arrays with given parameters.
Luis Martínez +2 more
doaj +1 more source