Construction of new codebook based on affine space over finite field

Journal of Civil Aviation University of China ›› 2021, Vol. 39 ›› Issue (3): 62-64.

• Basic Science • Previous Articles

Construction of new codebook based on affine space over finite field

LIU Xuemei, JIA Lihua

（College of Science, CAUC, Tianjin 300300, China）

Received:2020-10-17 Revised:2020-10-17 Accepted:2020-07-27 Online:2021-06-25 Published:2021-11-28

Abstract

Abstract: Codebooks are widely applied in code division multiple access systems to separate the signals of different users. Basing on the affine spaces over finite fields, a class of new codebooks are constructed. By the counting theorems of affine spaces, parameters of the codebook are obtained. Sufficient and necessary conditions for the codebooks are given to meet the Welch bound, and the conditions for the the maximum cross correlation amplitude astmptotically attains to the Welch bound are calculated.

Key words: finite field, affine space, codebook, Welch bound

CLC Number:

O236.2

LIU Xuemei, JIA Lihua. Construction of new codebook based on affine space over finite field [J]. Journal of Civil Aviation University of China, 2021, 39(3): 62-64.

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Construction of new codebook based on affine space over finite field

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