Advances in Mathematics of Communications (AMC)

Syndrome decoding for Hermite codes with a Sugiyama-type algorithm

Pages: 419 - 442, Volume 6, Issue 4, November 2012      doi:10.3934/amc.2012.6.419

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Irene I. Bouw - Institute of Pure Mathematics, Ulm University, Ulm, Germany (email)
Sabine Kampf - Institute of Communications Engineering, Ulm University, Ulm, Germany (email)

Abstract: This paper gives a new approach to decoding Hermite codes using the key equation, avoiding the use of majority voting. Our approach corrects up to $(d_{\min}-1)/2$ errors, and works up to some extent also beyond. We present an efficient implementation of our algorithm based on a Sugiyama-type iterative procedure for computing solutions of a key equation.

Keywords:  Hermite codes, algebraic decoding, Groebner bases.
Mathematics Subject Classification:  Primary: 14G50; Secondary: 11T71.

Received: July 2011;      Revised: May 2012;      Available Online: November 2012.