A mass formula for ℤ4 cyclic codes of length 2e

Taher Abualrub; Ali Ghrayeb; Robert H. Oehmke

doi:10.1109/ISIT.2004.1365524

A mass formula for ℤ₄ cyclic codes of length 2^e

Taher Abualrub
, Ali Ghrayeb
, Robert H. Oehmke

American University of Sharjah
Concordia University
University of Iowa

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Cyclic codes of length n = 2^e over the ring R₄ = Z₄[x]/(xⁿ - 1) are studied. A linear code C of length n over Z₄ is considered to be an additive submodule of the Z ₄-module Zⁿ₄. A cyclic code of length n over Z₄ is considered as an ideal in the ring R₄ = Z ₄[x]/xⁿ - 1. It is observed that the Hamming weight of a vector a ∈ Zⁿ₄ is the number of non-zero components in the vector.

Original language	English
Title of host publication	Proceedings - 2004 IEEE International Symposium on Information Theory
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	488
Number of pages	1
ISBN (Print)	0780382803
DOIs	https://doi.org/10.1109/ISIT.2004.1365524
Publication status	Published - 2004
Externally published	Yes
Event	2004 IEEE International Symposium on Information Theory, ISIT 2004 - Chicago, IL, United States Duration: 27 Jun 2004 → 2 Jul 2004

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8095

Conference

Conference	2004 IEEE International Symposium on Information Theory, ISIT 2004
Country/Territory	United States
City	Chicago, IL
Period	27/06/04 → 2/07/04

Access to Document

10.1109/ISIT.2004.1365524

Cite this

@inproceedings{d9603c016fcc4712a2be8cd4b078ae6b,

title = "A mass formula for ℤ4 cyclic codes of length 2e",

abstract = "Cyclic codes of length n = 2e over the ring R4 = Z4[x]/(xn - 1) are studied. A linear code C of length n over Z4 is considered to be an additive submodule of the Z 4-module Zn4. A cyclic code of length n over Z4 is considered as an ideal in the ring R4 = Z 4[x]/xn - 1. It is observed that the Hamming weight of a vector a ∈ Zn4 is the number of non-zero components in the vector.",

author = "Taher Abualrub and Ali Ghrayeb and Oehmke, \{Robert H.\}",

year = "2004",

doi = "10.1109/ISIT.2004.1365524",

language = "English",

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series = "IEEE International Symposium on Information Theory - Proceedings",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "488",

booktitle = "Proceedings - 2004 IEEE International Symposium on Information Theory",

address = "United States",

note = "2004 IEEE International Symposium on Information Theory, ISIT 2004 ; Conference date: 27-06-2004 Through 02-07-2004",

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Abualrub, T, Ghrayeb, A & Oehmke, RH 2004, A mass formula for ℤ₄ cyclic codes of length 2^e. in Proceedings - 2004 IEEE International Symposium on Information Theory. IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 488, 2004 IEEE International Symposium on Information Theory, ISIT 2004, Chicago, IL, United States, 27/06/04. https://doi.org/10.1109/ISIT.2004.1365524

A mass formula for ℤ₄ cyclic codes of length 2^e. / Abualrub, Taher; Ghrayeb, Ali; Oehmke, Robert H.
Proceedings - 2004 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc., 2004. p. 488 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Ghrayeb, Ali

AU - Oehmke, Robert H.

PY - 2004

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N2 - Cyclic codes of length n = 2e over the ring R4 = Z4[x]/(xn - 1) are studied. A linear code C of length n over Z4 is considered to be an additive submodule of the Z 4-module Zn4. A cyclic code of length n over Z4 is considered as an ideal in the ring R4 = Z 4[x]/xn - 1. It is observed that the Hamming weight of a vector a ∈ Zn4 is the number of non-zero components in the vector.

AB - Cyclic codes of length n = 2e over the ring R4 = Z4[x]/(xn - 1) are studied. A linear code C of length n over Z4 is considered to be an additive submodule of the Z 4-module Zn4. A cyclic code of length n over Z4 is considered as an ideal in the ring R4 = Z 4[x]/xn - 1. It is observed that the Hamming weight of a vector a ∈ Zn4 is the number of non-zero components in the vector.

UR - https://www.scopus.com/pages/publications/84888075970

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DO - 10.1109/ISIT.2004.1365524

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