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Title: Generalized Reed-Muller codes over ℤq
Authors: Bhaintwal, Maheshanand
Wasan S.K.
Published in: Designs, Codes, and Cryptography
Abstract: We have given a generalization of Reed-Muller codes over the prime power integer residue ring ℤq . 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 ℤq are also briefly discussed. It has been shown that GRM codes over ℤq 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. © 2009 Springer Science+Business Media, LLC.
Citation: Designs, Codes, and Cryptography (2010), 54(2): 149-166
Issue Date: 2010
Keywords: Codes over rings
Galois rings
GRM codes
Kerdock codes
ISSN: 9251022
Author Scopus IDs: 32867546000
Author Affiliations: Bhaintwal, M., Centre for Development of Advanced Computing, B-30, Sector-62, Noida 201307, India
Wasan, S.K., Department of Mathematics, Jamia Millia Islamia, New Delhi 110025, India
Corresponding Author: Bhaintwal, M.; Centre for Development of Advanced Computing, B-30, Sector-62, Noida 201307, India; email:
Appears in Collections:Journal Publications [MA]

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