Z4-linear Hadamard and extended perfect codes

If $N=2^k > 8$ then there exist exactly $[(k-1)/2]$ pairwise nonequivalent $Z_4$-linear Hadamard $(N,2N,N/2)$-codes and $[(k+1)/2]$ pairwise nonequivalent $Z_4$-linear extended perfect $(N,2^N/2N,4)$-codes. A recurrent construction of $Z_4$-linear Hadamard codes is given.Comment: 7p. WCC-200

Binary codes : binary codes databases

Combinatorics, Coding and Security Group (CCSG).The research group CCSG (Combinatorics, Coding and Security Group) is one of the research groups in the dEIC (Department of Information and Communications Engineering) at the UAB (Universitat Autònoma de Barcelona) in Spain. From 1987 the team CCSG has been uninterruptedly working in several projects and research activities on Information Theory, Communications, Coding Theory, Source Coding, Teledetection, Cryptography, Electronic Voting, e-Auctions, Mobile Agents, etc. The more important know-how of CCSG is about algorithms for forward error correction (FEC), such as Golay codes, Hamming product codes, Reed-Solomon codes, Preparata and Preparata-like codes, (extended) nonlinear 1-perfect codes, Z4-linear codes, Z2Z4-linear codes, etc.; computations of the rank and the dimension of the kernel for nonlinear codes as binary 1-perfect codes, q-ary 1-perfect codes, Preparata codes, Hadamard codes, Kerdock codes, quaternary Reed-Muller codes, etc.; the existence and structural properties for 1-perfect codes, uniformly packed codes, completely regular codes, completely transitive codes, etc..

Q-ary codes

The research group CCSG (Combinatorics, Coding and Security Group) is one of the research groups in the dEIC (Department of Information and Communications Engineering) at the UAB (Universitat Aut'onoma de Barcelona) in Spain. From 1987 the team CCSG has been uninterruptedly working in several projects and research activities on Information Theory, Communications, Coding Theory, Source Coding, Teledetection, Cryptography, Electronic Voting, e-Auctions, Mobile Agents, etc. The more important know-how of CCSG is about algorithms for forward error correction (FEC), such as Golay codes, Hamming product codes, Reed-Solomon codes, Preparata and Preparata-like codes, (extended) nonlinear 1-perfect codes, Z4-linear codes, Z2Z4-linear codes, etc.; computations of the rank and the dimension of the kernel for nonlinear codes as binary 1-perfect codes, q-ary 1-perfect codes, Preparata codes, Hadamard codes, Kerdock codes, quaternary Reed-Muller codes, etc.; the existence and structural properties for 1-perfect codes, uniformly packed codes, completely regular codes, completely transitive codes, etc