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Paper IDA.1.3
Paper Title Grassmannian Frames in Composite Dimensions by Exponentiating Quadratic Forms
Authors Renaud-Alexandre Pitaval, Yi Qin, Huawei Technologies Sweden AB, Sweden
Session A.1: Algebraic Coding Theory I
Presentation Lecture
Track Algebraic and Combinatorial Coding Theory
Manuscript  Click here to download the manuscript
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Abstract Grassmannian frames in composite dimensions D are constructed as a collection of orthogonal bases where each is the element-wise product of a mask sequence with a generalized Hadamard matrix. The set of mask sequences is obtained by exponentiation of a q-root of unity by different quadratic forms with m variables, where q and m are the product of the unique primes and total number of primes, respectively, in the prime decomposition of D. This method is a generalization of a well-known construction of mutually unbiased bases, as well as second-order Reed-Muller Grassmannian frames for power-of-two dimension D = 2^m, and allows to derive highly symmetric nested families of frames with finite alphabet. Explicit sets of symmetric matrices defining quadratic forms leading to constructions in non-prime-power dimension with good distance properties are identified.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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