Open AccessSelf-orthogonal Codes over Fq + uFq and Fq + uFq + u 2Fq
Author(s) -
Lucky Galvez,
Rowena Alma Betty,
Fidel R. Nemenzo
Publication year - 2020
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v13i4.3838
Subject(s) - mathematics , hermitian matrix , finite field , euclidean geometry , ring (chemistry) , euclidean distance , combinatorics , order (exchange) , discrete mathematics , pure mathematics , geometry , chemistry , organic chemistry , finance , economics
In this paper, we establish a mass formula for Euclidean and Hermitian self-orthogonal codes over the finite ring Fq + uFq, where Fq is the finite field of order q and u2 = 0. We also establish a mass formula for Euclidean self-orthogonal codes over the finite ring Fq + uFq + u2Fq, with u3 = 0 and characteristic of Fq is odd. These mass formulas are used to give a classification of Euclidean and Hermitian self-orthogonal codes over F2 + uF2 and F3 + uF3 of small lengths.