### Abstract

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

Original language | English |
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Pages (from-to) | 488 |

Number of pages | 1 |

Journal | IEEE International Symposium on Information Theory - Proceedings |

Publication status | Published - 2004 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*IEEE International Symposium on Information Theory - Proceedings*, 488.

**A mass formula for ℤ4 cyclic codes of length 2e
.** / Abualrub, Taher; Ghrayeb, Ali; Oehmke, Robert H.

Research output: Contribution to journal › Article

*IEEE International Symposium on Information Theory - Proceedings*, pp. 488.

}

TY - JOUR

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 Zn 4. 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 ∈ Zn 4 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 Zn 4. 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 ∈ Zn 4 is the number of non-zero components in the vector.

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

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

M3 - Article

SP - 488

JO - IEEE International Symposium on Information Theory - Proceedings

JF - IEEE International Symposium on Information Theory - Proceedings

SN - 2157-8097

ER -