http://repository.iitr.ac.in/handle/123456789/10259| 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 |
| URI: | https://doi.org/10.1007/s10623-009-9315-x http://repository.iitr.ac.in/handle/123456789/10259 |
| Issue Date: | 2010 |
| Keywords: | Codes over rings Galois rings GRM codes Kerdock codes |
| ISSN: | 9251022 |
| Author Scopus IDs: | 32867546000 8202044700 |
| 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: maheshanand@cdacnoida.in |
| Appears in Collections: | Journal Publications [MA] |
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