Dual product constructions of Reed - Muller type codes (Corresp.)

Author

Phelps, K.T.

Volume

Issue

fYear

1986

fDate

1/1/1986 12:00:00 AM

Firstpage

103

Lastpage

106

Abstract

Various linear and nonlinear $R(r,m)$ codes having parameters $(2^{m}, 2^{k}, 2^{m-r})$ with $k=\\sum _{i=0}^{r}\\left(^{m}_{i}\\right)$ are constructed from $R(r,q)$ and $R(r,p)$ codes, $m=p+q$ . A dual construction for $R(m-r,m)$ codes from $R(p-r,p)$ and $R(q-r,q)$ codes is also presented, $m=p+q$ . As a simple corollary we have that the number of nonequivalent $R(r,m)$ codes is at least exponential in the length (for $r> 1)$ . For $R(m-r,m)$ codes, the lower bound is doubly exponential in the length (for $r> 1)$ .

Keywords

Reed-Muller coding; Combinatorial mathematics; Heart; Linear code;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1986.1057123

Filename

1057123

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=941032