The Minimum Hamming Distance of Cyclic Codes of Length 2ps

2009-06-12
ÖZADAM, Hakan
Özbudak, Ferruh
We study cyclic codes of length 2p(s) over F-q where p is an odd prime. Using the results of [1], we compute the minimum Hamming distance of these codes.

Suggestions

A Bound on the Minimum Distance of Quasi-cyclic Codes
Gueneri, Cem; Özbudak, Ferruh (2012-01-01)
We give a general lower bound for the minimum distance of q-ary quasi-cyclic codes of length ml and index l, where m is relatively prime to q. The bound involves the minimum distances of constituent codes of length l as well as the minimum distances of certain cyclic codes of length m which are related to the fields over which the constituents are defined. We present examples which show that the bound is sharp in many instances. We also compare the performance of our bound against the bounds of Lally and Es...
The Concatenated Structure of Quasi-Cyclic Codes and an Improvement of Jensen's Bound
Guneri, Cem; Özbudak, Ferruh (2013-02-01)
Following Jensen's work from 1985, a quasi-cyclic code can be written as a direct sum of concatenated codes, where the inner codes are minimal cyclic codes and the outer codes are linear codes. We observe that the outer codes are nothing but the constituents of the quasi-cyclic code in the sense of Ling-Sole. This concatenated structure enables us to recover some earlier results on quasi-cyclic codes in a simple way, including one of our recent results which says that a quasi-cyclic code with cyclic constit...
Additive cyclic complementary dual codes over F4
Shi, Minjia; Liu, Na; Özbudak, Ferruh; Solé, Patrick (2022-10-01)
© 2022 Elsevier Inc.An additive cyclic code of length n over F4 can be defined equivalently as an F2[x]/〈xn+1〉-submodule of F4[x]/〈xn+1〉. In this paper we study additive cyclic and complementary dual codes of odd length over F4 with respect to the trace Hermitian inner product and the trace Euclidean inner product. We characterize subfield subcodes and trace codes of these codes by their generators as binary cyclic codes.
A NOTE ON NEGACYCLIC AND CYCLIC CODES OF LENGTH p(s) OVER A FINITE FIELD OF CHARACTERISTIC p
ÖZADAM, Hakan; Özbudak, Ferruh (American Institute of Mathematical Sciences (AIMS), 2009-08-01)
Recently, the minimum Hamming weights of negacyclic and cyclic codes of length p(s) over a finite field of characteristic p are determined in [4]. We show that the minimum Hamming weights of such codes can also be obtained immediately using the results of [1].
New cubic self-dual codes of length 54, 60 and 66
Comak, PINAR; Kim, Jon Lark; Özbudak, Ferruh (2018-08-01)
We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones. We consider the binary quasi-cyclic codes of length with the algebraic approach of Ling and Sol, (IEEE Trans Inf Theory 47(7):2751-2760, 2001. doi:. In particular, we improve the previous results by constructing 1 new binary [54, 27, 10], 6 new [60, 30, 12] and 50 new [66, 33, 12] cubic self-dual codes. We conjecture that there exist no more binary cubic self-dual codes with length 54, 60 and 66.
Citation Formats
H. ÖZADAM and F. Özbudak, “The Minimum Hamming Distance of Cyclic Codes of Length 2ps,” 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54359.