Images of Linear Block Codes over Fq+uFq+vFq+uvFq

Gray Images of Constacyclic Codes over some Polynomial Residue Rings

Let  be the quotient ring    where  is the finite field of size   and  is a positive integer. A Gray map  of length  over  is a special map from  to ( . The Gray map   is said to be a ( )-Gray map if the image of any -constacyclic code over    is a -constacyclic code over the field   . In this paper we investigate the existence of   ( )-Gray maps over . In this direction, we find an equivalent ...

Grassmannian Codes as Lifts of Matrix Codes Derived as Images of Linear Block Codes over Finite Fields

Let p be a prime such that p ≡ 2 or 3 (mod 5). Linear block codes over the non-commutative matrix ring M2(Fp) endowed with the Bachoc weight are derived as isometric images of linear block codes over the Galois field Fp2 endowed with the Hamming metric. When seen as rank metric codes, this family of matrix codes satisfies the Singleton bound and thus are maximum rank distance codes, which are t...

Isometries and Binary Images of Linear Block Codes over Z4+uZ4 and Z8+uZ8

Let F2 be the binary field and Z2r the residue class ring of integers modulo 2 , where r is a positive integer. For the finite 16-element commutative local Frobenius nonchain ring Z4 + uZ4, where u is nilpotent of index 2, two weight functions are considered, namely the Lee weight and the homogeneous weight. With the appropriate application of these weights, isometric maps from Z4 + uZ4 to the ...

Binary Linear Block Codes

Linear error-block codes

A linear error-block code is a natural generalization of the classical error-correcting code and has applications in experimental design, high-dimensional numerical integration and cryptography. This article formulates the concept of a linear error-block code and derives basic results for this kind of code by direct analogy to the classical case. Some problems for further research are raised. ©...