A polynomial-time probabilistic algorithm for the minimum distance of a non-binary linear error-correcting code
نویسنده
چکیده
The goal of the project is to examine a polynomial-time probabilistic algorithm to compute the minimum distance of an arbitrary, non-binary, linear error-correcting code. Only the binary case was done in A. Foster’s honors project [F]. For the non-binary case a new function was needed in the GAP kernel. This function was added by Steve Linton of St. Andrews, Scotland, one of GAP’s kernel maintainers, in August 2004. The programming shall be done in the GAP coding-theory package GUAVA. GAP is a computer algebra package whose open source kernel is written in the C programming language [GAP]. However, most packages (such as GUAVA) and the algorithms described here are written in GAP’s own interpreted language. Jointly, with my advisor, I extended Foster’s work (Algorithm 4) to the non-binary case but with a new feature making it faster (Algorithm 5). The paper ends with applications to the non-binary McEliece public key cryptosystem (see §4) and trace codes (see §3) Acknowledgement: The GAP examples were performed on an AMD-64 linux PC with 2G of RAM. I am grateful to the Director of Research Professor Reza Malek-Madani for making this available.
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