62,009 research outputs found
Fast Erasure-and-Error Decoding and Systematic Encoding of a Class of Affine Variety Codes
In this paper, a lemma in algebraic coding theory is established, which is
frequently appeared in the encoding and decoding for algebraic codes such as
Reed-Solomon codes and algebraic geometry codes. This lemma states that two
vector spaces, one corresponds to information symbols and the other is indexed
by the support of Grobner basis, are canonically isomorphic, and moreover, the
isomorphism is given by the extension through linear feedback shift registers
from Grobner basis and discrete Fourier transforms. Next, the lemma is applied
to fast unified system of encoding and decoding erasures and errors in a
certain class of affine variety codes.Comment: 6 pages, 2 columns, presented at The 34th Symposium on Information
Theory and Its Applications (SITA2011
AG codes from the second generalization of the GK maximal curve
The second generalized GK maximal curves are maximal
curves over finite fields with elements, where is a prime power
and an odd integer, constructed by Beelen and Montanucci. In this
paper we determine the structure of the Weierstrass semigroup where
is an arbitrary -rational point of . We
show that these points are Weierstrass points and the Frobenius dimension of
is computed. A new proof of the fact that the first and
the second generalized GK curves are not isomorphic for any is
obtained. AG codes and AG quantum codes from the curve are
constructed; in some cases, they have better parameters with respect to those
already known
Good Codes From Generalised Algebraic Geometry Codes
Algebraic geometry codes or Goppa codes are defined with places of degree
one. In constructing generalised algebraic geometry codes places of higher
degree are used. In this paper we present 41 new codes over GF(16) which
improve on the best known codes of the same length and rate. The construction
method uses places of small degree with a technique originally published over
10 years ago for the construction of generalised algebraic geometry codes.Comment: 3 pages, to be presented at the IEEE Symposium on Information Theory
(ISIT 2010) in Austin, Texas, June 201
- …