مرکز منطقه ای اطلاع رساني علوم و فناوري - Equidistant binary arithmetic codes (Corresp.)

DocumentCode :

941042

Title :

Equidistant binary arithmetic codes (Corresp.)

Author :

Clark, W. Edwin ; Liang, Joseph J.

Volume :

Issue :

fYear :

1986

fDate :

1/1/1986 12:00:00 AM

Firstpage :

106

Lastpage :

108

Abstract :

Let $C(B)$ denote the binary cyclic $AN$ code with generator $A$ , where $AB=2^{n} - 1$ . It is known that $C(B)$ is equidistant if $B$ is a prime power $p^{k}$ , where either $2$ or $-2$ is primitive modulo $B$ provided $p\\equiv 1 \\pmod {3}{\\rm \\if} k > 1$ . It is conjectured that these are the only $B$ such that $C(B)$ is equidistant. We have verified this for $B < 100 000$ . Several results are established that further limit the possibilities for counterexamples to the conjecture.