2011/10/07 by Marcus Greferath, Cathy Mc Fadden, Greferath, Marcus +4
Computer Science · Engineering · Mathematics · #05E99 #11T71 #94B05 #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1110.1538
openalex publication_date 2011/10/07 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
The Equivalence Theorem states that, for a given weight on the alphabet,\nevery linear isometry between linear codes extends to a monomial transformation\nof the entire space. This theorem has been proved for several weights and\nalphabets, including the original MacWilliams' Equivalence Theorem for the\nHamming weight on codes over finite fields. The question remains: What\nconditions must a weight satisfy so that the Extension Theorem will hold? In\nthis paper we provide an algebraic framework for determining such conditions,\ngeneralising the approach taken in [Greferath, Honold '06].\n