Modular and p-adic cyclic codes
Designs, Codes and Cryptography
On Generalized Hamming Weights for Galois Ring Linear Codes
Designs, Codes and Cryptography
Quaternary Codes
A Griesmer bound for linear codes over finite quasi-Frobenius rings
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
On Z2k-Linear and Quaternary Codes
SIAM Journal on Discrete Mathematics
On the weight hierarchy of Kerdock codes over Z4
IEEE Transactions on Information Theory
An efficient algorithm for constructing minimal trellises for codes over finite abelian groups
IEEE Transactions on Information Theory - Part 1
On the isometries between Z(pk) and Z pk
IEEE Transactions on Information Theory
Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes
IEEE Transactions on Information Theory
Gray isometries for finite chain rings and a nonlinear ternary (36, 312, 15) code
IEEE Transactions on Information Theory
Bounds on the minimum support weights
IEEE Transactions on Information Theory
| Hi-index | 0.01 |
In an earlier paper the authors studied simplex codes of type 驴 and β over $${\mathbb{Z}}_4$$ and obtained some known binary linear and nonlinear codes as Gray images of these codes. In this correspondence, we study weight distributions of simplex codes of type 驴 and β over $${\mathbb{Z}}_{{2^s}}.$$ The generalized Gray map is then used to construct binary codes. The linear codes meet the Griesmer bound and a few non-linear codes are obtained that meet the Plotkin/Johnson bound. We also give the weight hierarchies of the first order Reed-Muller codes over $${\mathbb{Z}}_{2^{s}}.$$ The above codes are also shown to satisfy the chain condition.