2009/01/01 by Hutchison, David, J. Pujol, Iwan Duursma +21 · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #Numerical Methods and Algorithms #Polynomial and algebraic computation #cs.IT #math.AG #math.IT #math.NT #msc:11T71 #msc:14G50 #msc:94B
paper · pdf · doi:10.1007/978-3-642-02181-7
published as J. Pujol, J. Rifa and L. Ronquillo. Construction of Additive Reed-Muller Codes. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, LNCS 5527 (June 2009), pages 223-226 · 7 pages, Part of the material in this paper was presented without proofs at the 18-th Symposium on Applied algebra, Algebraic algorithms, and Error Correcting Codes (AAECC 2009), Tarragona, Spain, June 8-12, 2009
openalex publication_date 2009/01/01 · arxiv created 2011/12/28 · arxiv updated 2011/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15
The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain families of Z2Z4-additive codes such that, under the Gray map, the corresponding binary codes have the same parameters and properties as the usual binary linear Reed-Muller codes. Moreover, the first family is the usual binary linear Reed-Muller family.