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- W2163670396 abstract "In this paper, Perfect Root-of-Unity Codes (PRUCs) with entries in α p = {x ∈ ℂ | xp = 1} where p is a prime are studied. A lower bound on the number of distinct phases in PRUCs over α p is derived. We show that PRUCs of length L ≥ p(p − 1) must use all phases in α p . It is also shown that if there exists a PRUC of length L over α p then p divides L. We derive equations (which we call principal equations) that give possible lengths of a PRUC over α p together with their phase distribution. Using these equations, we prove for example that the length of a 3-phase perfect code must be of the form equation for (h 1 , h 2 ) ∈ ℤ2 and we also give the exact number of occurences of each element from a3 in the code. Finally, all possible lengths (≤ 100) of PRUCs over α 5 and α 7 together with their phase distributions are provided." @default.
- W2163670396 created "2016-06-24" @default.
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- W2163670396 date "2011-05-01" @default.
- W2163670396 modified "2023-09-25" @default.
- W2163670396 title "Perfect Root-Of-Unity Codes with prime-size alphabet" @default.
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- W2163670396 doi "https://doi.org/10.1109/icassp.2011.5946360" @default.
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