caa a22 4500 605524157 CHVBK 20210128100752.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s10958-015-2347-z doi (NATIONALLICENCE)springer-10.1007/s10958-015-2347-z Tumaykin I. Lomonosov Moscow State University, Moscow, Russia aut Basic Reed-Muller Codes as Group Codes [Elektronische Daten] [I. Tumaykin] 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. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 206/6(2015-05-01), 699-710 1072-3374 206:6<699 2015 206 10958 https://doi.org/10.1007/s10958-015-2347-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2347-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Tumaykin I. Lomonosov Moscow State University, Moscow, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 206/6(2015-05-01), 699-710 1072-3374 206:6<699 2015 206 10958