Irfan Siap

Bio: Irfan Siap is an academic researcher from Yıldız Technical University. The author has contributed to research in topics: Linear code & Block code. The author has an hindex of 21, co-authored 106 publications receiving 1638 citations. Previous affiliations of Irfan Siap include University of Gaziantep & Ohio State University.

The Structure of 1-Generator Quasi-Twisted Codes and New Linear Codes

Abstract: One of the most important problems of coding theory is to construct codes with best possible minimum distances. Recently, quasi-cyclic (QC) codes have been proven to contain many such codes. In this paper, we consider quasi-twisted (QT) codes, which are generalizations of QC codes, and their structural properties and obtain new codes which improve minimum distances of best known linear codes over the finite fields GF(3) and GF(5). Moreover, we give a BCH-type bound on minimum distance for QT codes and give a sufficient condition for a QT code to be equivalent to a QC code.

Cyclic codes over the rings Z2 + uZ2 and Z2 + uZ2 + u2Z2

Abstract: In this paper, we study cyclic codes over the rings Z 2 + uZ 2 and Z 2 + uZ 2 + u 2 Z 2 . We find a set of generators for these codes. The rank, the dual, and the Hamming distance of these codes are studied as well. Examples of cyclic codes of various lengths are also studied.

Skew cyclic codes of arbitrary length

Abstract: In this paper, we study a special type of linear codes, called skew cyclic codes, in the most general case. This set of codes is a generalisation of cyclic codes but constructed using a non-commutative ring called the skew polynomial ring. In previous works, these codes have been studied with certain restrictions on their length. This work examines their structure for an arbitrary length without any restriction. Our results show that these codes are equivalent to either cyclic codes or quasi-cyclic codes, hence establish strong connections with well-known classes of codes.

Constacyclic codes over F2+uF2

Abstract: We study the structure of ( 1 + u ) -constacyclic codes of an arbitrary length n over the ring F 2 + uF 2 . We find a set of generators for each ( 1 + u ) -constacyclic code and its dual. We study the rank of cyclic codes and find their minimal spanning sets. We prove that the Gray image of a ( 1 + u ) -constacyclic code is a binary cyclic code of length 2 n . We conclude by giving examples of constacyclic codes and their Gray image binary codes. We give a direct construction of a [12,7,4] linear binary cyclic code that match the Hamming distance of the best binary code with length 12 and dimension 7.

$\BBZ_{2}\BBZ_{4}$ -Additive Cyclic Codes

Abstract: In this paper, we study Z2Z4-additive cyclic codes. These codes are identified as Z4[x]-submodules of the ring Rr,s=Z2[x]/〈xr-1〉×Z4[x]/〈xs-1〉. The algebraic structure of this family of codes is studied and a set of generator polynomials for this family as a Z4[x]-submodule of the ring Rr,s is determined. We show that the duals of Z2Z4-additive cyclic codes are also cyclic. We also present an infinite family of Maximum Distance separable with respect to the singleton bound codes. Finally, we obtain a number of binary linear codes with optimal parameters from the Z2Z4-additive cyclic codes.

[서평]「Applied Cryptography」

Abstract: The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind. The emphasis is on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity. Topics covered includes an introduction to the concepts in cryptography, attacks against cryptographic systems, key use and handling, random bit generation, encryption modes, and message authentication codes. Recommendations on algorithms and further reading is given in the end of the paper. This paper should make the reader able to build, understand and evaluate system descriptions and designs based on the cryptographic components described in the paper.

Constacyclic Codes and Some New Quantum MDS Codes

Abstract: One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. Quantum maximal distance separable (MDS) codes are optimal in the sense they attain maximal minimum distance. Recently, constructing quantum MDS codes has received much attention and seems to become more and more difficult. In this paper, based on classical constacyclic codes, we construct some new quantum MDS codes by employing the Hermitian construction. Compared with the known quantum MDS codes, these quantum MDS codes have much larger minimum distance.

Application of Constacyclic Codes to Quantum MDS Codes

Abstract: Quantum maximum-distance-separable (MDS) codes form an important class of quantum codes. To get q-ary quantum MDS codes, one of the effective ways is to find linear MDS codes C over F q2 satisfying C ⊥H ⊆ C, where C ⊥H denotes the Hermitian dual code of C. For a linear code C of length n over F q2 , we say that C is a dual-containing code if C ⊥H ⊆ C and C≠ F q2 n . Several classes of new quantum MDS codes with relatively large minimum distance have been produced through dual-containing constacyclic MDS codes. These works motivate us to make a careful study on the existence conditions for dual-containing constacyclic codes. We obtain necessary and sufficient conditions for the existence of dual-containing constacyclic codes. Four classes of dual-containing constacyclic MDS codes are constructed and their parameters are computed. Consequently, the quantum MDS codes are derived from these parameters. The quantum MDS codes exhibited here have minimum distance bigger than the ones available in the literature.