Bounding the trellis state complexity of algebraic geometric codes
| dc.creator | Munuera, Carlos | |
| dc.creator | Torres, Fernando | |
| dc.date | 2003-03-08 | |
| dc.date.accessioned | 2026-07-07T08:18:12Z | |
| dc.date.available | 2026-07-07T08:18:12Z | |
| dc.description | 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. | |
| dc.description | LaTeX, 14 pages, available at http://www.ime.unicamp.br/~ftorres | |
| dc.identifier | https://arxiv.org/abs/math/0303104 | |
| dc.identifier | http://arxiv.org/abs/math/0303104 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134353 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Information Theory | |
| dc.subject | 94B05, 94B27, 14G50 | |
| dc.title | Bounding the trellis state complexity of algebraic geometric codes | |
| dc.type | text |