m-adic residue codes

Author

Job, V.R.

Author_Institution

Dept. of Math. & Comput. Sci., Marymount Univ., Arlington, VA, USA

Volume

38

Issue

2

fYear

1992

fDate

3/1/1992 12:00:00 AM

Firstpage

496

Lastpage

501

Abstract

The m-adic residue codes are investigated and are found to have many of the strong properties of the quadratic residue codes. A subgroup of the automorphism group and restrictions on the form of the idempotents of the m-adic residue codes are given. It is shown that some m-adic residue codes are self-orthogonal and the duals of some m-adic residue codes are their complements. Bounds on the minimum of the weights of the odd-like vectors in the odd-like codes are given. At some lengths, m-adic residue codes exist for several values of m. Containment relationships between these codes are demonstrated which show that, when m is even, m-adic residue codes inherit properties of quadratic residue codes. A table is included that contains minimum weights of the binary m-adic residue codes of lengths less than or equal to 127.<>

Keywords

error correction codes; automorphism group; binary codes; containment relationships; duals; error correction codes; idempotents; m-adic residue codes; minimum weights; odd-like codes; odd-like vectors; quadratic residue codes; self-orthogonal codes; Binary codes; Error correction codes; Information theory; Mathematics; Polynomials; Terminology;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.119710

Filename

119710