Title :
On the Hamming weight of binary sequences and linear complexity
Author :
Sorokine, Vladislav ; Pasupat, Subbarayan
Author_Institution :
Qualcomm Inc., San Diego, CA, USA
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;
Conference_Titel :
Information Theory, 1998. Proceedings. 1998 IEEE International Symposium on
Conference_Location :
Cambridge, MA
Print_ISBN :
0-7803-5000-6
DOI :
10.1109/ISIT.1998.708690
