Result: A Relation Between Quasi-Cyclic Codes and 2-D Cyclic Codes

Title:
A Relation Between Quasi-Cyclic Codes and 2-D Cyclic Codes
Authors:
Guneri, Cem, Özbudak, Ferruh
Contributors:
Faculty of Engineering and Natural Sciences (Sabanci University), Sabanci University [Istanbul], Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University [Ankara] (METU)
Source:
WCC 2011 - Workshop on coding and cryptography. :203-208
Publisher Information:
HAL CCSD, 2011.
Publication Year:
2011
Collection:
collection:WCC2011
collection:TDS-MACS
collection:UNIV-MONTPELLIER
Subject Terms:
ACM: E.: Data, E.3: DATA ENCRYPTION, E.4: CODING AND INFORMATION THEORY, ACM: G.: Mathematics of Computing, G.2: DISCRETE MATHEMATICS, [INFO.INFO-CR]Computer Science [cs], Cryptography and Security [cs.CR], [INFO.INFO-DM]Computer Science [cs], Discrete Mathematics [cs.DM], [MATH.MATH-IT]Mathematics [math], Information Theory [math.IT], [INFO.INFO-IT]Computer Science [cs], Information Theory [cs.IT]
Subject Geographic:
Paris, France
Original Identifier:
HAL:
Document Type:
Conference conferenceObject<br />Conference papers
Language:
English
Access URL:
https://inria.hal.science/inria-00611777
https://inria.hal.science/inria-00611777/document
https://inria.hal.science/inria-00611777/file/54.pdf
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edshal.inria.00611777v1
Database:
HAL

Further Information

We consider a q-ary quasi-cyclic code C of length m' and index ', where both m and ' are relatively prime to q. If the constituents of C are cyclic codes, we show that C can also be viewed as a 2-D cyclic code of size m *l ' over Fq. If we further assume that m and ' are also coprime to each other, then we easily observe that the code C must be equivalent to a cyclic code. The last fact was proved earlier by Lim using a diff erent approach.