135 research outputs found
Counting generalized Reed-Solomon codes
In this article we count the number of generalized Reed-Solomon (GRS) codes
of dimension k and length n, including the codes coming from a non-degenerate
conic plus nucleus. We compare our results with known formulae for the number
of 3-dimensional MDS codes of length n=6,7,8,9
A new method for constructing small-bias spaces from Hermitian codes
We propose a new method for constructing small-bias spaces through a
combination of Hermitian codes. For a class of parameters our multisets are
much faster to construct than what can be achieved by use of the traditional
algebraic geometric code construction. So, if speed is important, our
construction is competitive with all other known constructions in that region.
And if speed is not a matter of interest the small-bias spaces of the present
paper still perform better than the ones related to norm-trace codes reported
in [12]
The Minimum Distance of Graph Codes
We study codes constructed from graphs where the code symbols are associated with the edges and the symbols connected to a given vertex are restricted to be codewords in a component code. In particular we treat such codes from bipartite expander graphs coming from Euclidean planes and other geometries. We give results on the minimum distances of the codes
Bounding the number of rational places using Weierstrass semigroups
Let Lambda be a numerical semigroup. Assume there exists an algebraic
function field over GF(q) in one variable which possesses a rational place that
has Lambda as its Weierstrass semigroup. We ask the question as to how many
rational places such a function field can possibly have and we derive an upper
bound in terms of the generators of Lambda and q. Our bound is an improvement
to a bound by Lewittes which takes into account only the multiplicity of Lambda
and q. From the new bound we derive significant improvements to Serre's upper
bound in the cases q=2, 3 and 4. We finally show that Lewittes' bound has
important implications to the theory of towers of function fields.Comment: 16 pages, 3 table
Decoding of concatenated codes with interleaved outer codes
Recently Bleichenbacher et al. proposed a decoding algorithm for interleaved (N, K) Reed-Solomon codes, which allows close to N-K errors to be corrected in many cases. We discuss the application of this decoding algorithm to concatenated codes
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