Systematic encoding of the Varshamov-Tenengol´ts codes and the Constantin-Rao codes

Author

Abdel-Ghaffar, Khaled A S ; Ferreira, Hendrik C.

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., Davis, CA, USA

Volume

44

Issue

1

fYear

1998

fDate

1/1/1998 12:00:00 AM

Firstpage

340

Lastpage

345

Abstract

The maximum number of information bits that can be encoded systematically by the number-theoretic codes of Varshamov and Tenengol´ts (1965) is determined. This number is also studied for the more general class of the group-theoretic Constantin-Rao (1979) codes. Although these codes are at least as large as the Varshamov-Tenengol´ts codes, it is shown that the number of bits that can be systematically encoded using a Constantin-Rao code does not exceed the number of bits that can be systematically encoded using a Varshamov-Tenengol´ts code. In fact, in many cases, the largest Constantin-Rao code has the least number of bits that can be systematically encoded

Keywords

binary sequences; decoding; error correction codes; group theory; number theory; Varshamov-Tenengol´ts codes; binary asymmetric error correcting codes; decoding; group-theoretic Constantin-Rao codes; information bits; nonlinear codes; number-theoretic codes; systematic encoding; Decoding; Encoding; Error correction codes; Laboratories; Linear code; Notice of Violation; Upper bound; Welding;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.651063

Filename

651063