Results 11 to 20 of about 154,729 (273)
IEEE Transactions on Information Theory, 2011 In network coding a constant dimension code consists of a set of k-dimensional subspaces of F_q^n. Orbit codes are constant dimension codes which are defined as orbits of a subgroup of the general linear group, acting on the set of all subspaces of F_q^n.
Braun, Michael +3 more
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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
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Cyclic Sieving for cyclic codes [PDF]
Finite Fields and Their Applications, 2021 Prompted by a question of Jim Propp, this paper examines the cyclic sieving phenomenon (CSP) in certain cyclic codes. For example, it is shown that, among dual Hamming codes over $F_q$, the generating function for codedwords according to the major index statistic (resp. the inversion statistic) gives rise to a CSP when $q=2$ or $q=3$ (resp. when $q=2$).
Alex Mason +2 more
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Describing a cyclic code by another cyclic code [PDF]
2012 IEEE International Symposium on Information Theory Proceedings, 2012 A new approach to bound the minimum distance of $q$-ary cyclic codes is presented. The connection to the BCH and the Hartmann--Tzeng bound is formulated and it is shown that for several cases an improvement is achieved. We associate a second cyclic code to the original one and bound its minimum distance in terms of parameters of the associated code.
Alexander Zeh, Sergey Bezzateev
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Cyclic and Convolutional Codes With Locality [PDF]
IEEE Transactions on Information Theory, 2021 An extended abstract of this work appears in Proceedings of the 2020 IEEE International Symposium on Information Theory (ISIT 2020)
Zitan Chen, Alexander Barg
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CoRR, 2020 arXiv admin note: text overlap with arXiv:1906 ...
Güneri, Cem, Ling, San, Özkaya, Buket
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Designs, Codes and Cryptography, 2021 In network coding, a flag code is a set of sequences of nested subspaces of $\mathbb{F}_q^n$, being $\mathbb{F}_q$ the finite field with $q$ elements. Flag codes defined as orbits of a cyclic subgroup of the general linear group acting on flags of $\mathbb{F}_q^n$ are called cyclic orbit flag codes.
Clementa Alonso-González +1 more
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On quasi-cyclic codes as a generalization of cyclic codes
Finite Fields and Their Applications, 2012 In this article we see quasi-cyclic codes as block cyclic codes. We generalize some properties of cyclic codes to quasi-cyclic ones such as generator polynomials and ideals. Indeed we show a one-to-one correspondence between l-quasi-cyclic codes of length m and ideals of M_l(Fq)[X]/(X^m-1).
Morgan Barbier +2 more
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On Cyclic Convolutional Codes [PDF]
Acta Applicandae Mathematica, 2004 50 ...
Gluesing-Luerssen, Heide +1 more
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On the exponent of cyclic codes
CoRR, 2022 We propose an algorithm to find a lower bound for the number of cyclic codes over any finite field with any given exponent. Besides, we give a formula to find the exponent of BCH codes.
Anuj Kumar Bhagat, Ritumoni Sarma
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