200 research outputs found
On Coset Weight Distributions of the 3-Error-Correcting BCH- Codes
Résumé disponible dans le fichier PD
The coset weight distributions of certain BCH codes and a family of curves
We study the distribution of the number of rational points in a family of
curves over a finite field of characteristic 2. This distribution determines
the coset weight distribution of a certain BCH code.Comment: Plain Tex, 15 pages; some numerical data adde
On the binary weight distribution of some Reed-Solomon codes
Consider an (n,k) linear code with symbols from GF(2 sup M). If each code symbol is represented by a m-tuple over GF(2) using certain basis for GF(2 sup M), a binary (nm,km) linear code is obtained. The weight distribution of a binary linear code obtained in this manner is investigated. Weight enumerators for binary linear codes obtained from Reed-Solomon codes over GF(2 sup M) generated by polynomials, (X-alpha), (X-l)(X-alpha), (X-alpha)(X-alpha squared) and (X-l)(X-alpha)(X-alpha squared) and their extended codes are presented, where alpha is a primitive element of GF(2 sup M). Binary codes derived from Reed-Solomon codes are often used for correcting multiple bursts of errors
Binary Cyclic Codes from Explicit Polynomials over \gf(2^m)
Cyclic codes are a subclass of linear codes and have applications in consumer
electronics, data storage systems, and communication systems as they have
efficient encoding and decoding algorithms. In this paper, monomials and
trinomials over finite fields with even characteristic are employed to
construct a number of families of binary cyclic codes. Lower bounds on the
minimum weight of some families of the cyclic codes are developed. The minimum
weights of other families of the codes constructed in this paper are
determined. The dimensions of the codes are flexible. Some of the codes
presented in this paper are optimal or almost optimal in the sense that they
meet some bounds on linear codes. Open problems regarding binary cyclic codes
from monomials and trinomials are also presented.Comment: arXiv admin note: substantial text overlap with arXiv:1206.4687,
arXiv:1206.437
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