Designs and their codes
Modular and p-adic cyclic codes
Designs, Codes and Cryptography
Quaternary Codes
The Mathematical Theory of Coding
The Mathematical Theory of Coding
On quasi-cyclic codes over $${\mathbb{Z}_q}$$
Applicable Algebra in Engineering, Communication and Computing
Cyclic codes and quadratic residue codes over Z4
IEEE Transactions on Information Theory
The permutation group of affine-invariant extended cyclic codes
IEEE Transactions on Information Theory - Part 2
Generalized Reed-Muller codes and power control in OFDM modulation
IEEE Transactions on Information Theory
A transform approach to permutation groups of cyclic codes over Galois rings
IEEE Transactions on Information Theory
Quasi-cyclic codes over Z4 and some new binary codes
IEEE Transactions on Information Theory
Affine invariant extended cyclic codes over Galois rings
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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We have given a generalization of Reed---Muller codes over the prime power integer residue ring $${\mathbb{Z}_q}$$ . These codes are analogs of generalized Reed---Muller (GRM) codes over finite fields. We mainly focus on primitive GRM codes, which are basically a generalization of Quaternary Reed---Muller (QRM) codes. We have also given a multivariate representation of these codes. Non-primitive GRM codes over $${\mathbb{Z}_q}$$ are also briefly discussed. It has been shown that GRM codes over $${\mathbb{Z}_q}$$ are free extended cyclic codes. A trace description of these codes is also given. We have obtained formulas for their ranks and also obtained expressions for their minimum Hamming distances.