Alltop math

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Alltop math

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(PDF) A Family of Alltop Functions that are EA

  • Theory 26 (3):350-354, 1980) described a set of sequences based on a cubic function and showed that these functions were optimal with respect to …

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[1302.4498] A family of Alltop functions that are EA

  • Sequences with optimal correlation properties are much sought after for applications in communication systems
  • Theory 26(3):350-354, 1980) described a set of sequences based on a cubic function and showed that these functions were optimal with respect to known bounds on auto and crosscorrelation

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[PDF] Complex sequences with low periodic correlations

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A family of Alltop functions that are EA-inequivalent to

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[1205.3310v1] Planar Difference Functions

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AfamilyofAlltopfunctionsthatare EA

  • Lemma 4 holds for Alltop functions: Lemma 5
  • Let L(x) be an additive polynomial, then the following are equiva-lent
  • (i) A(L(x)) is an Alltop polynomial
  • (ii) L(A(x)) is an Alltop polynomial
  • (iii) A(x) is an Alltop polynomial and L(x) is a permutation polynomial
  • Follows closely the proof of Lemma 4 as published in [6, Lem 2.3]

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[1205.3310] Planar Difference Functions

  • In 1980 Alltop produced a family of cubic phase sequences that nearly meet the Welch bound for maximum non-peak correlation magnitude
  • This family of sequences were shown by Wooters and Fields to be useful for quantum state tomography
  • Alltop's construction used a function that is not planar, but whose difference function is planar

Arxiv.org   DA: 9 PA: 14 MOZ Rank: 44

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[1205.3310v2] Planar Difference Functions

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  • This family of sequences were shown by Wooters and Fields to be useful for quantum state tomography
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