مرکز منطقه ای اطلاع رساني علوم و فناوري - New family of single-error correcting codes

DocumentCode :

914710

Title :

New family of single-error correcting codes

Author :

Sloane, Neil J A ; Whitehead, Donald S.

Volume :

Issue :

fYear :

1970

fDate :

11/1/1970 12:00:00 AM

Firstpage :

717

Lastpage :

719

Abstract :

A construction is given that combines an $(n, M_1, d_1)$ code with an $(n, M_2, d_2 = [frac{1}{2}(d_1 + 1)])$ code to form a $(2n, M_1 M_2, d_1)$ code. This is used to construct a new family of nongroup single-error correcting codes of all lengths $n$ from $2^m$ to 3 · $2^{m-1} - 1$ , for every $m \\geq 3$ . These codes have more codewords than any group code of the same length and minimum distance. A number of other nongroup codes are also obtained. Examples of the new codes are (16,2560,3) and (16,36,7) codes, both having more codewords than any comparable group code.