Conjectural permutation decoding of some AG codes
David A. Joyner · ACM SIGSAM Bulletin · 2005
We study the action of a finite group on the Riemann-Roch space of certain divisors on a specific hyperelliptic curve X defined over a finite field with "large" automorphism group G . If D and E = P l + ... + P n are G -equivariant divisors on X ( P i ∈ X ( F )) then G acts on associated AG code C = C ( D,E ) by permuting coordinates. This note discusses the permutation decoding of these AG codes. The main "results" are conjectures regarding the complexity of the permutation decoding of these hyperelliptic codes. The open source GAP error-correcting codes package GUAVA is used to compute examples.