The Minimum Hamming Distance of Cyclic Codes of Length 2ps

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.


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...
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...
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].
Repeated - root cyclic codes and matrix product codes
Özadam, Hakan; Özbudak, Ferruh; Department of Cryptography (2012)
We study the Hamming distance and the structure of repeated-root cyclic codes, and their generalizations to constacyclic and polycyclic codes, over finite fields and Galois rings. We develop a method to compute the Hamming distance of these codes. Our computation gives the Hamming distance of constacyclic codes of length $np^s$\ in many cases. In particular, we determine the Hamming distance of all constacyclic, and therefore cyclic and negacyclic, codes of lengths p^s and 2p^s over a finite field of charac...
On a class of repeated root monomial like abelian codes
Martinez Moro, Edgar; Özadam, Hakan; Özbudak, Ferruh; szabo, steve (2015-04-01)
In this paper we study polycyclic codes of length p s 1 × ⋯ × p s n p ​s ​1 ​​ ​​ ×⋯×p ​s ​n ​​ ​​ \ over $\F_{p^a}$\ generated by a single monomial. These codes form a special class of abelian codes. We show that these codes arise from the product of certain single variable codes and we determine their minimum Hamming distance. Finally we extend the results of Massey et. al. in \cite{MASSEY_1973} on the weight retaining property of monomials in one variable to the weight retaining property of monomials ...
Citation Formats
H. ÖZADAM and F. Özbudak, “The Minimum Hamming Distance of Cyclic Codes of Length 2ps,” 2009, Accessed: 00, 2020. [Online]. Available: