A Construction of Codebooks Asymptotically Meeting the Levenshtein Bound

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  • YAN Zhangti
    School of Mathematics, Southwest Jiaotong University
  • GU Zhi
    School of Mathematics, Southwest Jiaotong University
  • GUO Wei
    School of Mathematics, Southwest Jiaotong University
  • WANG Jianpeng
    School of Mathematics, Southwest Jiaotong University

抄録

<p>Codebooks with small maximal cross-correlation amplitudes have important applications in code division multiple access (CDMA) communication, coding theory and compressed sensing. In this letter, we design a new codebook based on a construction of Ramanujan graphs over finite abelian groups. We prove that the new codebook with length K=q+1 and size N=q2+2q+2 is asymptotically optimal with nearly achieving the Levenshtein bound when n=3, where q is a prime power. The parameters of the new codebook are new.</p>

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