Group of Isometries of Niederreiter-Rosenbloom-Tsfasman Block Space

• Autor(a) principal: PANEK,LUCIANO
• Data de Publicação: 2020
• Outros Autores: PANEK,NAYENE MICHELE PAIÃO
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512020000200271
• topic: error-block metric; poset metric; Niederreiter-Rosenbloom-Tsfasman metric; ordered Hamming metric; isometries; automorphisms

ABSTRACT Let P = 1 , 2 , . . . , n ≤ be a poset that is an union of disjoint chains of the same length and V = F q N be the space of N-tuples over the finite field F q. Let V i = F q k i , with 1 ≤ i ≤ n, be a family of finite-dimensional linear spaces such that k 1 + k 2 + . . . + k n = N and let V = V 1 × V 2 × . . . × V n endow with the poset block metric d P , π induced by the poset P and the partition π = k 1 , k 2 , . . . , k n, encompassing both Niederreiter-Rosenbloom-Tsfasman metric and error-block metric. In this paper, we give a complete description of group of isometries of the metric space V , d P , π, also called the Niederreiter-Rosenbloom-Tsfasman block space. In particular, we reobtain the group of isometries of the Niederreiter-Rosenbloom-Tsfasman space and obtain the group of isometries of the error-block metric space.