Codebooks from generalized bent Z_4-valued quadratic forms
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Codebooks with small inner-product correlation have application in unitary space-time modulations, multiple description coding over erasure channels, direct spread code division multiple access communications, compressed sensing, and coding theory. It is interesting to construct codebooks (asymptotically) achieving the Welch bound or the Levenshtein bound. This paper presented a class of generalized bent Z_4-valued quadratic forms, which contain functions of Heng and Yue (Optimal codebooks achieving the Levenshtein bound from generalized bent functions over Z_4. Cryptogr. Commun. 9(1), 41-53, 2017). By using these generalized bent Z_4-valued quadratic forms, we constructs optimal codebooks achieving the Levenshtein bound. These codebooks have parameters (2^2m+2^m,2^m) and alphabet size 6.
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