A general key equation based on elementary symmetric functions is developed for decoding some binary error control codes. Here, the syndrome is obtained by computing the elementary symmetric functions (instead of the power-sums) of the received word. It is then shown that the new key equation can be used to efficiently decode wide classes of binary codes. A new class of codes is introduced in this paper which can correct up to t0 0 → 1 errors and, simultaneously, up to t1 1 → 0 errors. The new key equation can be used to decode the new class of codes and some known codes such as some t-asymmetric error correcting (t-AEC) codes, the t-symmetric error correcting (t-SEC) BCH codes and Goppa codes. Some new lower-bounds on the number of codewords in minimum asymmetric distance d codes are derived. Some generalizations to the non binary case are also given.
On decoding some error control codes using the elementary symmetric functions
TALLINI, Luca
;
2010-01-01
Abstract
A general key equation based on elementary symmetric functions is developed for decoding some binary error control codes. Here, the syndrome is obtained by computing the elementary symmetric functions (instead of the power-sums) of the received word. It is then shown that the new key equation can be used to efficiently decode wide classes of binary codes. A new class of codes is introduced in this paper which can correct up to t0 0 → 1 errors and, simultaneously, up to t1 1 → 0 errors. The new key equation can be used to decode the new class of codes and some known codes such as some t-asymmetric error correcting (t-AEC) codes, the t-symmetric error correcting (t-SEC) BCH codes and Goppa codes. Some new lower-bounds on the number of codewords in minimum asymmetric distance d codes are derived. Some generalizations to the non binary case are also given.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
