On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings
Designs, Codes and Cryptography
Codes over rings, complex lattices and Hermitian modular forms
European Journal of Combinatorics
Linear Codes over $\mathbb{F}_{q}[u]/(u^s)$ with Respect to the Rosenbloom---Tsfasman Metric
Designs, Codes and Cryptography
On the Algebraic Structure of Quasi-cyclic Codes IV: Repeated Roots
Designs, Codes and Cryptography
Designs, Codes and Cryptography
Weights modulo pe of linear codes over rings
Designs, Codes and Cryptography
Linear codes over $${\mathbb{F}_2+u\mathbb{F}_2+v\mathbb{F}_2+uv\mathbb{F}_2}$$
Designs, Codes and Cryptography
Cyclic codes over R=Fp+uFp+...+uk-1Fp with length psn
Information Sciences: an International Journal
Designs, Codes and Cryptography
On the decomposition of self-dual codes over F2+uF2 with an automorphism of odd prime order
Finite Fields and Their Applications
Codes over Rk, Gray maps and their binary images
Finite Fields and Their Applications
Self-dual codes over F2+uF2 with an automorphism of odd order
Finite Fields and Their Applications
On the classification and enumeration of self-dual codes
Finite Fields and Their Applications
Finite Fields and Their Applications
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The alphabet F2+uF2 is viewed here as a quotient of the Gaussian integers by the ideal (2). Self-dual F2 +uF2 codes with Lee weights a multiple of 4 are called Type II. They give even unimodular Gaussian lattices by Construction A, while Type I codes yield unimodular Gaussian lattices. Construction B makes it possible to realize the Leech lattice as a Gaussian lattice. There is a Gray map which maps Type II codes into Type II binary codes with a fixed point free involution in their automorphism group. Combinatorial constructions use weighing matrices and strongly regular graphs. Gleason-type theorems for the symmetrized weight enumerators of Type II codes are derived. All self-dual codes are classified for length up to 8. The shadow of the Type I codes yields bounds on the highest minimum Hamming and Lee weights