Bounding the trellis state complexity of algebraic geometric codes

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Let C be an algebraic geometric code of dimension k and length n constructed on a curve X over $F_q$. Let s(C) be the state complexity of C and set w(C):=min{k,n-k}, the Wolf upper bound on s(C). We introduce a numerical function R that depends on the gonality sequence of X and show that s(C)\geq w(C)-R(2g-2), where g is the genus of X. As a matter of fact, R(2g-2)\leq g-(γ_2-2) with γ_2 being the gonality over F_q of X, and thus in particular we have that s(C)\geq w(C)-g+γ_2-2.
LaTeX, 14 pages, available at http://www.ime.unicamp.br/~ftorres

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Algebraic Geometry, Information Theory, 94B05, 94B27, 14G50

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http://salesiana.dossiersoluciones.com/handle/123456789/134353

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0303104
 http://arxiv.org/abs/math/0303104

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arXiv