✦ LIBER ✦

Duadic Z4-Codes

✍ Scribed by Philippe Langevin; Patrick Solé

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 158 KB
Volume: 6
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.2000.0285

No coin nor oath required. For personal study only.

✦ Synopsis

The structure of abelian Z -codes (and more generally Z N K -codes) is studied. The approach is spectral: discrete Fourier transform and idempotents. A criterion for self-duality is derived. An arithmetic test on the length for the existence of nontrivial abelian self-dual codes is derived. A natural generalization of both the supplemented quadratic residue codes and the binary duadic codes is introduced. Isodual abelian Z codes are considered, constructed, and used to produce 4-modular lattices.

2000

📜 SIMILAR VOLUMES

Shadow Codes over Z4

✍ Steven T. Dougherty; Masaaki Harada; Patrick Solé 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 371 KB

The notion of a shadow of a self-dual binary code is generalized to self-dual codes over 9 . A Gleason formula for the symmetrized weight enumerator of the shadow of a Type I code is derived. Congruence properties of the weights follow; this yields constructions of self-dual codes of larger lengths

Bounds for Self-Dual Codes Over Z4

✍ Eric Rains 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 137 KB

New bounds are given for the minimal Hamming and Lee weights of self-dual codes over 9 . For a self-dual code of length n, the Hamming weight is bounded above by 4[n/24]#f (n mod 24), for an explicitly given function f; the Lee weight is bounded above by 8[n/24]#g(n mod 24), for a di!erent function

On the Optimal Z4 Codes of Type II and L

On the Optimal Z4 Codes of Type II and Length 16

✍ I.M. Duursma; M. Greferath; S.E. Schmidt 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 82 KB

codes of type II and length 16 are known. In this note we relate the five optimal codes to the octacode. We also construct an optimal quaternary iso-dual [14, code which was not known previously.

Classification of Type IV Self-Dual Z4-C

Classification of Type IV Self-Dual Z4-Codes of Length 16

✍ Masaaki Harada; Akihiro Munemasa 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 129 KB

The classi"cation of all self-dual codes over 9 of length up to 15 and Type II codes of length 16 is known. In this note, we give a method to classify Type IV self-dual codes over 9 . As an application, we present the classi"cation of Type IV self-dual codes of length 16. There are exactly 11 inequ

Z8-Cyclic Codes and Quadratic Residue Co

Z8-Cyclic Codes and Quadratic Residue Codes

✍ Mei Hui Chiu; Stephen S.-T Yau; Yung Yu 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 160 KB

In memory of Professor Gian-Carlo Rota for his great contributions in combinatorial and discrete geometry A set of n-tuples over 8 is called a code over 8 or a 8 code if it is a 8 module. A particularly interesting family of 8 -cyclic codes are quadratic residue codes. We define such codes in terms

Code zéro

✍ Follett, Ken 📂 Fiction 📅 1999 🌐 French ⚖ 174 KB 👁 1 views