193 research outputs found
The second Feng-Rao number for codes coming from telescopic semigroups
In this manuscript we show that the second Feng-Rao number of any telescopic
numerical semigroup agrees with the multiplicity of the semigroup. To achieve
this result we first study the behavior of Ap\'ery sets under gluings of
numerical semigroups. These results provide a bound for the second Hamming
weight of one-point Algebraic Geometry codes, which improves upon other
estimates such as the Griesmer Order Bound
Cyclotomic numerical semigroups
Given a numerical semigroup , we let be its semigroup polynomial. We study cyclotomic numerical semigroups;
these are numerical semigroups such that has all its roots
in the unit disc. We conjecture that is a cyclotomic numerical semigroup if
and only if is a complete intersection numerical semigroup and present some
evidence for it. Aside from the notion of cyclotomic numerical semigroup we
introduce the notion of cyclotomic exponents and polynomially related numerical
semigroups. We derive some properties and give some applications of these new
concepts.Comment: 17 pages, accepted for publication in SIAM J. Discrete Mat
Weight hierarchies of a family of linear codes associated with degenerate quadratic forms
We restrict a degenerate quadratic form over a finite field of odd
characteristic to subspaces. Thus, a quotient space related to is
introduced. Then we get a non-degenerate quadratic form induced by over the
quotient space. Some related results on the subspaces and quotient space are
obtained. Based on this, we solve the weight hierarchies of a family of linear
codes related to Comment: 12 page
An Introduction to Algebraic Geometry codes
We present an introduction to the theory of algebraic geometry codes.
Starting from evaluation codes and codes from order and weight functions,
special attention is given to one-point codes and, in particular, to the family
of Castle codes
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