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Let R r = F q + v 1 F F q + ··· + v r F q , where q is the power of prime, v i 2 = v i , v i v j = v j v i = 0 for 1 ≤ i, j ≤ r and r ≥ 1. In this paper, the structure of λ-constacyclic codes over the ring R r is studied and a Gray map ϕ from R r n to F q (r +1) n is given. The necessary and sufficient conditions for these codes to contain their Euclidean duals are determined. As an application, we obtain many new better quantum codes from dual-containing λ-constacyclic codes over R r , for r = 1, 2, 3, that improve the known existing quantum codes. [ABSTRACT FROM AUTHOR]

Recently certain few-Lee weight additive codes over some mixed alphabet rings with optimal or minimal Gray images are constructed using suitable defining sets. Inspired by these works, we construct two special classes of linear codes over Z 2 [ u ] with u 2 = 0 by using the mixed alphabet ring Z 2 Z 2 [ u ] and employing simplicial complexes having one or more maximal elements. We show that these codes have few-Lee weights by determining their Lee weight distributions. As applications, we are getting the 1st order binary Reed-Muller codes of length 2 3 m − 2 (where m > 1) and some infinite families of binary self-orthogonal minimal codes via Gray map. [ABSTRACT FROM AUTHOR]

Abstract: We determine self-orthogonal designs and self-orthogonal codes from the primitive representations of the projective symplectic groups and , respectively. We establish some properties of these codes and the nature of some classes of codewords. Some of the codes are optimal or near optimal for the given length and dimension. The dual codes of some designs and those of some complementary designs admit majority logic decoding. [Copyright &y& Elsevier]

Abstract: All binary projective codes of dimension up to 6 are classified. Information about the number of the codes with different minimum distances and automorphism group orders is given. [Copyright &y& Elsevier]

Abstract: We study a class of codes with good parameters and their duals explicitly. We give direct constructions of the dual codes and obtain self-orthogonal codes with good parameters. [Copyright &y& Elsevier]

Abstract: The binary optimal self-orthogonal codes of dimension and length are classified. They are used for constructing self-dual codes of lengths 40, 42, and 44. All optimal binary self-dual codes of lengths 42 and 44 which have an automorphism of order 5 with four independent cycles are obtained up to equivalence. All optimal self-dual codes of lengths 40, 42 and 44 which have an automorphism of order 3 with six independent cycles are constructed. Some of them are the first known codes with their weight enumerators. [Copyright &y& Elsevier]

In this paper, we consider a method for constructing non-binary self-orthogonal codes from symmetric designs with fixed-point-free automorphisms. All codes over GF(3) and GF(7) derived from symmetric 2-(v,k,λ) designs with fixed-point-free automorphisms of order p for the parameters (v,k,λ,p)=(27,14,7,3),(40,27,18,5) and (45,12,3,5) are classified. A ternary [63,20,21] code with a record breaking minimum weight is constructed from the symmetric 2-(189,48,12) design found recently by Janko. Several codes over GF(5) and GF(7) that are either optimal or have the largest known minimum weight are constructed from designs obtained from known difference sets. [Copyright &y& Elsevier]

Let F q be the finite field of order q , where q is a power of an odd prime p , and p , ℓ are distinct odd primes, and m , n , K are positive integers. In this paper, the multiplicative group F q ∗ = F q ∖ { 0 } is decomposed into mutually disjoint union of gcd (2 K ℓ m , q − 1) cosets of the cyclic group generated by ξ 2 K ℓ m p n , where ξ is a primitive element of F q. With the help of this decomposition, all constacyclic codes of length 2 K ℓ m p n over F q are classified into gcd (2 K ℓ m , q − 1) disjoint classes. Accordingly, generator polynomials of constacyclic codes of length 2 K ℓ m p n over the finite field F q and their duals are explicitly determined in the cases, when q ≡ ± 1 (mod 2 K). And also some complementary-dual, self-orthogonal, self-dual, dual-containing constacyclic codes of length 2 K ℓ m p n over F q are determined. [ABSTRACT FROM AUTHOR]