A key equation and the computation of error values for codes from order domains

Details A key equation and the computation of error values for codes from order domains A key equation and the computation of error values for codes from order domains

2003-03-24

arxiv.org/abs/math/0303299v2

Mathematics

Commutative Algebra

25 pages; Several references added and typographical errors corrected

Scientific paper

We study the computation of error values in the decoding of codes constructed from order domains. Our approach is based on a sort of analog of the key equation for decoding Reed-Solomon and BCH codes. We identify a key equation for all codes from order domains which have finitely-generated value semigroups; the field of fractions of the order domain may have arbitrary transcendence degree, however. We provide a natural interpretation of the construction using the theory of Macaulay's inverse systems and duality. O'Sullivan's generalized Berlekamp-Massey-Sakata (BMS) decoding algorithm applies to the duals of suitable evaluation codes from these order domains. When the BMS algorithm does apply, we will show how it can be understood as a process for constructing a collection of solutions of our key equation.

Affiliated with

Also associated with

No associations

Rating

A key equation and the computation of error values for codes from order domains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A key equation and the computation of error values for codes from order domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A key equation and the computation of error values for codes from order domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-332826