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On Optimal and Proper Binary Codes from Irreducible Cyclic Codes over GF(2m)
Katsumi SAKAKIBARA Ritsuko IWASA Yoshiharu YUBA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 1999/10/25
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
binary images, irreducible cyclic codes over GF(2m), optimal codes, Griesmer bound, proper codes, undetected error probability,
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We prove that binary images of irreducible cyclic codes C over GF(2m) and binary concatenated codes of C and a binary [m+1,m,2] even-parity code are optimal (in the sense that they meet the Griesmer bound with equality) and proper, if a root of the check polynomial of C is primitive over GF(2m) or its extensions.