2019/06/10 by Ronald Orozco López, López, Ronald Orozco
Computer Science · Engineering · Mathematics · #05B20 #05E15 #94B60 #Action (physics) #Arithmetic #Binary number #Coding theory and cryptography #Combinatorics #Combinatorics (math.CO) #Cyclic permutation #Discrete mathematics #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Information Theory (cs.IT) #Mathematics #Permutation (music) #Permutation group #Physics #Ring (chemistry) #Symmetric group #cs.IT #graph theory and CDMA systems #math.CO #math.GR #math.IT #msc:05B20 #msc:05E15 #msc:94B60
paper · pdf · doi:10.48550/arxiv.1906.04250
published in arXiv (Cornell University) (Cornell University) · 22 pages
arxiv created 2019/06/10 · openalex publication_date 2019/06/10 · arxiv updated 2019/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper the relationship between S-subgroups in \Z2n and binary codes is shown. If the codes used are both P(T)-codes and G-codes, then the S-subgroup is free. The codes constructed are cyclic, decimated or symmetric and the S-subgroups obtained are free under the action the cyclic permutation subgroup, invariants under the action the decimated permutation subgroup and symmetric under the action of symmetric permutation subgroup, respectively. Also it is shows that there is no codes generating whole \Z2n in any \Gn(a)-complete S-set of the S-ring \mathfrakS(\Z2n,Sn).