2010/04/10 by Iwan Duursma, Duursma, Iwan, Radoslav Kirov +1 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Coding theory and cryptography #Cryptography and Residue Arithmetic #Error Correcting Code Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #cs.IT #math.AG #math.IT #math.NT
paper · pdf · doi:10.48550/arxiv.1004.1752
openalex publication_date 2010/04/10 · arxiv created 2011/02/17 · arxiv updated 2011/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One-point codes on the Hermitian curve produce long codes with excellent parameters. Feng and Rao introduced a modified construction that improves the parameters while still using one-point divisors. A separate improvement of the parameters was introduced by Matthews considering the classical construction but with two-point divisors. Those two approaches are combined to describe an elementary construction of two-point improved codes. Upon analysis of their minimum distance and redundancy, it is observed that they improve on the previous constructions for a large range of designed distances.