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   Vol.E82-A   No.10   pp.2191-2193
Publication Date: 1999/10/25
Online ISSN: 
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.