On cyclic MDS codes of length q over GF(q)
IEEE Transactions on Information Theory
Handbook of Coding Theory
On the Algebraic Structure of Quasi-cyclic Codes IV: Repeated Roots
Designs, Codes and Cryptography
Repeated-root cyclic and negacyclic codes over a finite chain ring
Discrete Applied Mathematics - Special issue: Coding and cryptography
A note on the q-ary image of a qm-ary repeated-root cyclic code
IEEE Transactions on Information Theory
Cyclic codes and self-dual codes over F2+uF2
IEEE Transactions on Information Theory
Decoding of cyclic codes over F2+uF2
IEEE Transactions on Information Theory
Negacyclic codes over Z4 of even length
IEEE Transactions on Information Theory
Weight distributions of cyclic self-dual codes
IEEE Transactions on Information Theory
On the generators of Z4 cyclic codes of length 2e
IEEE Transactions on Information Theory
Cyclic and negacyclic codes over finite chain rings
IEEE Transactions on Information Theory
A mass formula and rank of Z4 cyclic codes of length 2e
IEEE Transactions on Information Theory
Negacyclic codes of length 2s over galois rings
IEEE Transactions on Information Theory
Complete Distances of All Negacyclic Codes of Length 2s Over Z2a
IEEE Transactions on Information Theory
On the decomposition of self-dual codes over F2+uF2 with an automorphism of odd prime order
Finite Fields and Their Applications
Finite Fields and Their Applications
| Hi-index | 754.84 |
We study all constacyclic codes of length 2sover GR(R, m), the Galois extension ring of dimension m of the ring R = F2 + uF2. The units of the ring GR(R, m) are of the forms α, and α + uβ, where α, β are nonzero elements of F2m, which correspond to 2m (2m - 1) such constacyclic codes. First, the structure and Hamming distances of (1 + uγ)-constacyclic codes are established. We then classify all cyclic codes of length 2s over GR(R, m), and obtain a formula for the number of those cyclic codes, as well as the number of codewords in each code. Finally, one-to-one correspondences between cyclic and α-constacyclic codes, as well as (1 + uγ)-constacyclic and (α + uβ)-constacyclic codes are provided via ring isomorphisms, that allow us to carry over the results about cyclic and (1 + uγ)-constacyclic accordingly to all constacyclic codes of length 2sover GR(R, m).