On Linear Complexity and Schaub Bound for Cyclic Codes by Defining Sequence with Unknown Elements

Junru ZHENG  Takayasu KAIDA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.9   pp.2337-2340
Publication Date: 2006/09/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.9.2337
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section on Sequence Design and its Application in Communications)
Category: 
Keyword: 
cyclic code,  defining sequence,  minimum distance,  lower bound,  Schaub algorithm,  unknown element,  

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Summary: 
The Schaub bound is one of well-known lower bounds of the minimum distance for given cyclic code C, and defined as the minimum value, which is a lower bound on rank of matrix corresponding a codeword, in defining sequence for all sub-cyclic codes of given code C. In this paper, we will try to show relationships between the Schaub bound, the Roos bound and the shift bound from numerical experiments. In order to reduce computational time for the Schaub bound, we claim one conjecture, from numerical examples in binary and ternary cases with short code length that the Schaub bound can be set the value from only defining sequence of given code C.