Basic Reed-Muller Codes as Group Codes
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| 024 | 7 | 0 | |a 10.1007/s10958-015-2347-z |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10958-015-2347-z | ||
| 100 | 1 | |a Tumaykin |D I. |u Lomonosov Moscow State University, Moscow, Russia |4 aut | |
| 245 | 1 | 0 | |a Basic Reed-Muller Codes as Group Codes |h [Elektronische Daten] |c [I. Tumaykin] |
| 520 | 3 | |a Reed-Muller codes are one of the most well-studied families of codes; however, there are still open problems regarding their structure. Recently, a new ring-theoretic approach has emerged that provides a rather intuitive construction of these codes. This approach is centered around the notion of basic Reed-Muller codes. We recall that Reed-Muller codes over a prime field are radical powers of a corresponding group algebra. In this paper, we prove that basic Reed-Muller codes in the case of a nonprime field of arbitrary characteristic are distinct from radical powers. This implies the same result for regular codes. Also we show how to describe the inclusion graph of basic Reed-Muller codes and radical powers via simple arithmetic equations. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 773 | 0 | |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 206/6(2015-05-01), 699-710 |x 1072-3374 |q 206:6<699 |1 2015 |2 206 |o 10958 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10958-015-2347-z |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10958-015-2347-z |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Tumaykin |D I. |u Lomonosov Moscow State University, Moscow, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 206/6(2015-05-01), 699-710 |x 1072-3374 |q 206:6<699 |1 2015 |2 206 |o 10958 | ||