A product construction for perfect codes over arbitrary alphabets (Corresp.)

Author

Phelps, Kevin T.

Volume

Issue

fYear

1984

fDate

9/1/1984 12:00:00 AM

Firstpage

769

Lastpage

771

Abstract

A general product construction for perfect single-error-correcting codes over an arbitrary alphabet is presented. Given perfect single-error-correcting codes of lengths $n, m$ , and $q + 1$ over an alphabet of order $q$ , one can construct perfect single-error-correcting codes of length $(q - 1)nm + n + m$ over the same alphabet. Moreover, if there exists a perfect single-error-correcting code of length $q + 1$ over an alphabet of order $q$ , then there exist perfect single-error-correcting codes of length $n$ , $n = (q^{t} _ 1)/(q - 1)$ , and $(t > 0$ , an integer). Finally, connections between projective planes of order $q$ and perfect codes of length $q + 1$ over an alphabet of order $q$ are discussed.

Keywords

Error-correction coding; Automatic control; Binary sequences; Decoding; Error correction codes; Hamming distance; Particle separators; Process control;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1984.1056963

Filename

1056963

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=939392