مرکز منطقه ای اطلاع رساني علوم و فناوري - Dual product constructions of Reed

DocumentCode :

941032

Title :

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.ricest.ac.ir/dl/search/defaultta.aspx?DTC=49&DC=941032