Abstract
Exponential sums over Galois rings have many applications in coding theory, cryptography and algebraic combinatorics. In this article, we employ additive characters and multiplicative characters over Galois rings to present two classes of codebooks, and prove that these codebooks asymptotically achieve the Welch bound. In addition, the resulting codebooks have new parameters.
Highlights
INTRODUCTIONMany researchers concern about constructing asymptotically codebooks that meet the Welch bound, i.e., the maximum cross-correlation amplitude asymptotically achieves the Welch bound for a sufficiently large length of vectors
An (N, K ) codebook C = {c0, c1, · · ·, cN−1} is a set of N unit norm 1 × K complex vectors
Sun et al.: Two New Classes of Codebooks Asymptotically Achieving the Welch Bound article, we propose two new constructions of complex codebooks by using additive characters and multiplicative characters over Galois rings
Summary
Many researchers concern about constructing asymptotically codebooks that meet the Welch bound, i.e., the maximum cross-correlation amplitude asymptotically achieves the Welch bound for a sufficiently large length of vectors. S. Sun et al.: Two New Classes of Codebooks Asymptotically Achieving the Welch Bound article, we propose two new constructions of complex codebooks by using additive characters and multiplicative characters over Galois rings. Sun et al.: Two New Classes of Codebooks Asymptotically Achieving the Welch Bound article, we propose two new constructions of complex codebooks by using additive characters and multiplicative characters over Galois rings Results show that these codebooks are asymptotically optimal with respect to the Welch bound.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
