On a necessary condition for L-step orthogonalization of linear codes and its applications

Duc N.Q. (1973) On a necessary condition for L-step orthogonalization of linear codes and its applications. Information and Control, 22 2: 123-131. doi:10.1016/S0019-9958(73)90219-2


Author Duc N.Q.
Title On a necessary condition for L-step orthogonalization of linear codes and its applications
Journal name Information and Control
ISSN 0019-9958
Publication date 1973
Sub-type Article (original research)
DOI 10.1016/S0019-9958(73)90219-2
Volume 22
Issue 2
Start page 123
End page 131
Total pages 9
Subject 2200 Engineering
Abstract By generalizing a known result for double-error-correcting binary primitive Bose\3-Chaudhuri\3-Hocquenghem codes, the following statement is proved: A necessary condition for L-step orthogonalization of a t-error-correcting binary linear code C of length n is given by n ≥ {if123-1} + {if123-2} if its expurgated version C′ is distinct from C, and n ≥ {if123-3} if C′ is identical to C, where {if123-4} is the minimum distance of the dual {if123-5} of the code C′, and {if123-6} is that of the dual {if123-7} of the code C′, expurgated from C by a single information digit. From this result, it is found that the following codes cannot be L-step orthogonalized: triple-error-correcting BCH codes with odd m greater than 5 and even m equal to 8 and 10, all the BCH codes with m = 7 except two trivial cases, and most of the binary quadratic residue codes with known minimum Hamming distances. In addition, various codes are analyzed; and where possible, the types of majority-logic decoding are tabulated for these codes, namely, a class of binary cyclic codes of length n ≤ 43 and all the binary BCH codes of length n = 63.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import
 
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