15 citations · 60 across the 17 of their papers we have counts for
5 papers · 2 filters
List Decoding of Hermitian Codes using Groebner Bases
Kwankyu Lee, Michael E. O'Sullivan
List decoding of Hermitian codes is reformulated to allow an efficient and simple algorithm for the interpolation step. The algorithm is developed using the theory of Groebner base…
Redundancies of Correction-Capability-Optimized Reed-Muller Codes
Maria Bras-Amorós, Michael E. O'Sullivan
This article is focused on some variations of Reed-Muller codes that yield improvements to the rate for a prescribed decoding performance under the Berlekamp-Massey-Sakata algorith…
On Semigroups Generated by Two Consecutive Integers and Improved Hermitian Codes
Maria Bras-Amorós, Michael E. O'Sullivan
Analysis of the Berlekamp-Massey-Sakata algorithm for decoding one-point codes leads to two methods for improving code rate. One method, due to Feng and Rao, removes parity checks…
The Order Bound on the Minimum Distance of the One-Point Codes Associated to a Garcia-Stichtenoth Tower of Function Fields
Maria Bras-Amorós, Michael E. O'Sullivan
Garcia and Stichtenoth discovered two towers of function fields that meet the Drinfeld-Vlăduţ bound on the ratio of the number of points to the genus. For one of these towers, Garc…
Duality for Several Families of Evaluation Codes
Maria Bras-Amorós, Michael E. O'Sullivan
We consider generalizations of Reed-Muller codes, toric codes, and codes from certain plane curves, such as those defined by norm and trace functions on finite fields. In each case…