DocumentCode
2453937
Title
On the Hamming weight of binary sequences and linear complexity
Author
Sorokine, Vladislav ; Pasupat, Subbarayan
Author_Institution
Qualcomm Inc., San Diego, CA, USA
fYear
1998
fDate
16-21 Aug 1998
Firstpage
103
Abstract
It is shown that the Hamming weight of a binary sequence can be determined from the rank defect of an appropriate Bezoutian matrix. The rank defect of a Hankel matrix for a linear recurring sequence obtained from the Mattson-Solomon polynomial of the “time domain” sequence, is a function of the Hamming weight of the sequence. As applications of these ideas, we derive an extension of a theorem by MacWilliams and Sloane (1977) regarding the Hamming weight of sequences, and prove a result similar to that of Chien (1972) and Blahut
Keywords
Hankel matrices; binary sequences; encoding; polynomials; Bezoutian matrix; Hamming weight; Hankel matrix; Mattson-Solomon polynomial; binary sequences; linear complexity; linear recurring sequence; rank defect; time domain sequence; Binary sequences; Character generation; Codes; Councils; Educational institutions; Error correction; Hamming weight; Linear algebra; Polynomials; Vectors;
fLanguage
English
Publisher
ieee
Conference_Titel
Information Theory, 1998. Proceedings. 1998 IEEE International Symposium on
Conference_Location
Cambridge, MA
Print_ISBN
0-7803-5000-6
Type
conf
DOI
10.1109/ISIT.1998.708690
Filename
708690
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