𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Minimal Cyclic Codes of Length 2pn

✍ Scribed by S.K. Arora; Manju Pruthi

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
97 KB
Volume
5
Category
Article
ISSN
1071-5797

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we completely describe the 2n#2 minimal cyclic codes of length 2pL over F O , as minimal ideals in the ring R"F O [x]/1xN L !12 in terms of their generating idempotents. Explicit expressions for the primitive idempotents, generating polynomials, minimum distance, and dimension of these codes are obtained. We assume that F O "GF(q), where q (prime power) is primitive root modulo 2pL and n51 is an integer, and both p and q are odd.

πŸ“œ SIMILAR VOLUMES

Minimal Codes of Prime-Power Length
Minimal Codes of Prime-Power Length
✍ Manju Pruthi; S.K. Arora πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 247 KB

Explicit expressions for the (n Ο© 1) primitive idempotents in FG (the group algebra of the cyclic group G of order p n (p odd prime, n ΟΎ 1) over the finite field F of prime power order q where q is a primitive root modulo p n ) are obtained. The minimum distance, the dimension, and the generating po

Optimal binary covering codes of length
Optimal binary covering codes of length 2j
✍ William D. Weakley πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 144 KB

## Abstract The minimum size of a binary covering code of length __n__ and covering radius __r__ is denoted by __K__(__n__,__r__), and codes of this length are called optimal. For __j__ > 0 and __n__ = 2^__j__^, it is known that __K__(__n__,1) = 2 · __K__(__n__βˆ’1,1) = 2^__nβ€‰βˆ’β€‰j__^. Say that two bin

Weight Behavior of Irreducible Cyclic BW
Weight Behavior of Irreducible Cyclic BWD-Codes
✍ J.-P. Zanotti πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 280 KB

In Langevin and Zanotti (1995), we introduced a new class of codes called balanced weight distribution (BWD)-codes, with the remarkable property that their weight distribution is balanced, i.e., there are the same number of codewords for each non-zero weight. The aim of this paper is to study the we

Classification of Type IV Self-Dual Z4-C
Classification of Type IV Self-Dual Z4-Codes of Length 16
✍ Masaaki Harada; Akihiro Munemasa πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 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