New Completely Regular q-ary Codes Based on Kronecker Products

• Published in: IEEE transactions on information theory Vol. 56; no. 1; pp. 266 - 272
• Main Authors: Rifa, J., Zinoviev, V.A.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-01-2010; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Arrays; Code standards; Codes; Completely regular codes; completely transitive codes; Computation; Construction; Construction equipment; Covering; covering radius; Cryptography; Data encryption; Error correction codes; H infinity control; Information theory; Integers; intersection numbers; Kronecker product; Linear code; Parity check codes; uniformly packed codes; Vectors
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2009.2034812

For any integer ¿ ¿ 1 and for any prime power q , an explicit construction of an infinite family of completely regular (and completely transitive) q-ary codes with d = 3 and with covering radius ¿ is given. The intersection array is also computed. Under the same conditions, the explicit construction of an infinite family of q-ary uniformly packed codes (in the wide sense) with covering radius ¿, which are not completely regular, is also given. In both constructions, the Kronecker product is the basic tool that has been used.