Duadic Codes

Author

Leon, Jeffrey S. ; Masley, John M. ; Pless, Vera

Volume

Issue

fYear

1984

fDate

9/1/1984 12:00:00 AM

Firstpage

709

Lastpage

714

Abstract

A new family of binary cyclic $(n,(n + 1)/2)$ and $(n,(n - 1)/2)$ codes are introduced, which include quadratic residue (QR) codes when $n$ is prime. These codes are defined in terms of their idempotent generators, and they exist for all odd $n = p_{1}^{a_{1}} p_{2}^{a_{2}} \\cdots p_{r}^{a_{r}}$ where each $p_{i}$ is a prime $\\equiv pm 1 \\pmod {8}$ . Dual codes are identified. The minimum odd weight of a duadic $(n,(n + 1)/2)$ code satisfies a square root bound. When equality holds in the sharper form of this bound, vectors of minimum weight hold a projective plane. The unique projective plane of order 8 is held by the minimum weight vectors in two inequivalent $(73,37,9)$ duadic codes. All duadic codes of length less than $127$ are identified, and the minimum weights of their extensions are given. One of the duadic codes of length $113$ has greater minimum weight than the QR code of that length.

Keywords

Cyclic coding; Dual coding; Residue coding; Binary sequences; Circuits; Computer science; Feedback; Mathematics; Notice of Violation; Shift registers; Statistics; Terminology;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1984.1056944

Filename

1056944

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=939211