Labelings of Lee and Hamming spaces
Discrete Mathematics
Some constacyclic codes over Z2k and binary quasi-cyclic codes
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
On Linear Codes over$${\mathbb{Z}}_{2^{s}}$$
Designs, Codes and Cryptography
Trading Inversions for Multiplications in Elliptic Curve Cryptography
Designs, Codes and Cryptography
Designs, Codes and Cryptography
Some constructions of systematic authentication codes using galois rings
Designs, Codes and Cryptography
The linear programming bound for codes over finite Frobenius rings
Designs, Codes and Cryptography
On the Quasi-cyclicity of the Gray Map Image of a Class of Codes over Galois Rings
ICMCTA '08 Proceedings of the 2nd international Castle meeting on Coding Theory and Applications
On the Gray Image of Cyclic Codes over Finite Chain Rings
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Improved p-ary codes and sequence families from Galois rings
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
A class of constacyclic codes over Zpm
Finite Fields and Their Applications
Some families of Z4-cyclic codes
Finite Fields and Their Applications
Homogeneous weights and exponential sums
Finite Fields and Their Applications
On the groups of units of finite commutative chain rings
Finite Fields and Their Applications
Orthogonality Matrices for Modules over Finite Frobenius Rings and MacWilliams' Equivalence Theorem
Finite Fields and Their Applications
New ring-linear codes from dualization in projective Hjelmslev geometries
Designs, Codes and Cryptography
| Hi-index | 754.84 |
Using tensor product constructions for the first-order generalized Reed-Muller codes, we extend the well-established concept of the Gray isometry between (Z4, δL) and (Z2 2, δH) to the context of finite chain rings. Our approach covers previous results by Carlet (see ibid., vol.44, p.1543-7, 1998), Constantinescu (see Probl. Pered. Inform., vol.33, no.3, p.22-8, 1997 and Ph.D. dissertation, Tech. Univ. Munchen, Munchen, Germany, 1995), Nechaev et al. (see Proc. IEEE Int. Symp. Information Theory and its Applications, p.31-4, 1996) and overlaps with Heise et al. (see Proc. ACCT 6, Pskov, Russia, p.123-9, 1998) and Honold et al. (see Proc. ACCT 6, Pskov, Russia, p.135-41, 1998). Applying the Gray isometry on Z9 we obtain a previously unknown nonlinear ternary (36, 312, 15) code