A mass formula for ℤ4 cyclic codes of length 2e

Taher Abualrub; Ali Ghrayeb; Robert H. Oehmke

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

Taher Abualrub, Ali Ghrayeb, Robert H. Oehmke

Research output: Contribution to journal › Conference article › 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
Pages (from-to)	488
Number of pages	1
Journal	IEEE International Symposium on Information Theory - Proceedings
Publication status	Published - 2004
Externally published	Yes
Event	Proceedings - 2004 IEEE International Symposium on Information Theory - Chicago, IL, United States Duration: 27 Jun 2004 → 2 Jul 2004

Cite this

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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",

language = "English",

pages = "488",

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

issn = "2157-8095",

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

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

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T1 - A mass formula for ℤ4 cyclic codes of length 2e

AU - Abualrub, Taher

AU - Ghrayeb, Ali

AU - Oehmke, Robert H.

PY - 2004

Y1 - 2004

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 - http://www.scopus.com/inward/record.url?scp=84888075970&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:84888075970

SN - 2157-8095

SP - 488

JO - IEEE International Symposium on Information Theory - Proceedings

JF - IEEE International Symposium on Information Theory - Proceedings

T2 - Proceedings - 2004 IEEE International Symposium on Information Theory

Y2 - 27 June 2004 through 2 July 2004

ER -

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

Abstract

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