Studies on the distribution of the shortest linear recurring sequences
Information Sciences: an International Journal
On the joint linear complexity profile of explicit inversive multisequences
Journal of Complexity
On minimal polynomials over Fqm and over Fq of a finite-length sequence over F qm
Finite Fields and Their Applications
Lattice basis reduction algorithms and multi-dimensional continued fractions
Finite Fields and Their Applications
Multi-continued fraction algorithm and generalized B--M algorithm over Fq
Finite Fields and Their Applications
Finite Fields and Their Applications
Bounds on collaborative decoding of interleaved Hermitian codes and virtual extension
Designs, Codes and Cryptography
Fast skew-feedback shift-register synthesis
Designs, Codes and Cryptography
Decoding interleaved Reed---Solomon codes beyond their joint error-correcting capability
Designs, Codes and Cryptography
| Hi-index | 754.84 |
A generalization of the Berlekamp-Massey algorithm is presented for synthesizing minimum length linear feedback shift registers for generating prescribed multiple sequences. A more general problem is first considered, that of finding the smallest initial set of linearly dependent columns in a matrix over an arbitrary field, which includes the multisequence problem as a special case. A simple iterative algorithm, the fundamental iterative algorithm (FIA), is presented for solving this problem. The generalized algorithm is then derived through a refinement of the FIA. Application of this generalized algorithm to decoding cyclic codes up to the Hartmann-Tzeng (HT) bound and Roos bound making use of multiple syndrome sequences is considered. Conditions for guaranteeing that the connection polynomial of the shortest linear feedback shift register obtained by the algorithm will be the error-locator polynomial are determined with respect to decoding up to the HT bound and special cases of the Roos bound