A mass formula and rank of ℤ4 cyclic codes of length 2 e

Taher Abualrub; Ali Ghrayeb; Robert H. Oehmke

doi:10.1109/TIT.2004.838109

A mass formula and rank of ℤ₄ cyclic codes of length 2 ^e

Taher Abualrub^*, Ali Ghrayeb, Robert H. Oehmke

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

28 Citations (Scopus)

Abstract

In this correspondence, we study cyclic codes of length n = 2 ^e over the ring R₄ = ℤ₄[χ ⌉/(χⁿ - 1). In particular, we derive a closed-form expression for the number of these codes for a given length n. We also study the rank of these codes and derive an expression for that. Furthermore, we give an example in which we study all cyclic codes of length 8. We also study all self-dual codes of length 8 and 16 and classify them according to their type.

Original language	English
Pages (from-to)	3306-3312
Number of pages	7
Journal	IEEE Transactions on Information Theory
Volume	50
Issue number	12
DOIs	https://doi.org/10.1109/TIT.2004.838109
Publication status	Published - Dec 2004
Externally published	Yes

Keywords

Cyclic codes
Dual codes
Self-dual codes

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10.1109/TIT.2004.838109

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AU - Ghrayeb, Ali

AU - Oehmke, Robert H.

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N2 - In this correspondence, we study cyclic codes of length n = 2 e over the ring R4 = ℤ4[χ ⌉/(χn - 1). In particular, we derive a closed-form expression for the number of these codes for a given length n. We also study the rank of these codes and derive an expression for that. Furthermore, we give an example in which we study all cyclic codes of length 8. We also study all self-dual codes of length 8 and 16 and classify them according to their type.

AB - In this correspondence, we study cyclic codes of length n = 2 e over the ring R4 = ℤ4[χ ⌉/(χn - 1). In particular, we derive a closed-form expression for the number of these codes for a given length n. We also study the rank of these codes and derive an expression for that. Furthermore, we give an example in which we study all cyclic codes of length 8. We also study all self-dual codes of length 8 and 16 and classify them according to their type.

KW - Cyclic codes

KW - Dual codes

KW - Self-dual codes

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U2 - 10.1109/TIT.2004.838109

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JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 12

ER -

A mass formula and rank of ℤ₄ cyclic codes of length 2 ^e

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Keywords

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