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- Abelian group (2)
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- Backward shift operator (1)
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- Elliptic Curve Cryptography (1)
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- Frequency division multiplexing (1)
- Golay codes (1)
- Hadamard (1)
- Hadamard difference set (1)
- Mathematics (1)
- McFarland (1)
- Nonabelian group (1)
- Novel β-Polyfluoroalkoxy Vinamidinium Salts (1)
- Out-of-phase periodic autocorrelation coefficients (1)
- Perfect binary array (1)
- Power control (1)
- Pseudocontinuations (1)
- Quantum Computing (1)
- Reed-Muller codes (1)
- Relative difference sets (1)
- Shor’s algorithm (1)
- Simplex code (1)
- Spence parameter families (1)
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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
A Unifying Construction For Difference Sets, James A. Davis, Jonathan Jedwab
A Unifying Construction For Difference Sets, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
We present a recursive construction for difference sets which unifies the Hadamard, McFarland, and Spence parameter families and deals with all abelian groups known to contain such difference sets. The construction yields a new family of difference sets with parameters (v, k, λ,n)=(22d+4(22d+2−1)/3, 22d+1(22d+3+1)/3, 22d+1(22d+1+1)/3, 24d+2) for d⩾0. The construction establishes that a McFarland difference set exists in an abelian group of order 22 …
Pseudocontinuations And The Backward Shift, Alexandru Aleman, Stefan Richter, William T. Ross
Pseudocontinuations And The Backward Shift, Alexandru Aleman, Stefan Richter, William T. Ross
Department of Math & Statistics Technical Report Series
In this paper, we will examine the backward shift operator Lƒ = (ƒ – ƒ(0))/z on certain Banach spaces of analytic functions on the open unit disk D. In particular, for a (closed) subspace M for which LM ⊂ M, we wish to determine the spectrum, the point spectrum, and the approximate point spectrum of L|M. In order to do this, we will use the concept of "pseudocontinuation" of functions across the unit circle ∏.
Using The Quantum Computer To Break Elliptic Curve Cryptosystems, Jodie Eicher, Yaw Opoku
Using The Quantum Computer To Break Elliptic Curve Cryptosystems, Jodie Eicher, Yaw Opoku
Department of Math & Statistics Technical Report Series
This article gives an introduction to Elliptic Curve Cryptography and Quantum Computing. It includes an analysis of Peter Shor’s algorithm for the quantum computer breakdown of Discrete Log Cryptosystems and an analog to Shor’s algorithm for Elliptic Curve Cryptosystems. An extended example is included which illustrates how this modified Shor’s algorithm will work.
Nested Hadamard Difference Sets, James A. Davis, Jonathan Jedwab
Nested Hadamard Difference Sets, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
A Hadamard difference set (HDS) has the parameters (4N2, 2N2 − N, N2 − N). In the abelian case it is equivalent to a perfect binary array, which is a multidimensional matrix with elements ±1 such that all out-of-phase periodic autocorrelation coefficients are zero. We show that if a group of the form H × Z2pr contains a (hp2r, √hpr(2√hpr − 1), √hpr(√hpr − 1)) HDS (HDS), p a prime not dividing |H| …
Using The Simplex Code To Construct Relative Difference Sets In 2-Groups, James A. Davis, Surinder K. Sehgal
Using The Simplex Code To Construct Relative Difference Sets In 2-Groups, James A. Davis, Surinder K. Sehgal
Department of Math & Statistics Faculty Publications
Relative Difference Sets with the parameters (2a, 2b, 2a, 2a-b) have been constructed many ways (see [2], [3], [5], [6], and [7] for examples). This paper modifies an example found in [1] to construct a family of relative difference sets in 2-groups that gives examples for b = 2 and b = 3 that have a lower rank than previous examples. The Simplex code is used in the construction.
Peak-To-Mean Power Control And Error Correction For Ofdm Transmission Using Golay Sequences And Reed-Muller Codes, James A. Davis, J Jedwab
Peak-To-Mean Power Control And Error Correction For Ofdm Transmission Using Golay Sequences And Reed-Muller Codes, James A. Davis, J Jedwab
Department of Math & Statistics Faculty Publications
A coding scheme for OFDM transmission is proposed, exploiting a previously unrecognised connection between pairs of Golay complementary sequences and second-order Reed-Muller codes. The scheme solves the notorious problem of power control in OFDM systems by maintaining a peak-to-mean envelope power ratio of at most 3dB while allowing simple encoding and decoding at high code rates for binary, quaternary or higher-phase signalling together with good error correction.
Efficient And General Synthesis Of Novel Β-Polyfluoroalkoxy Vinamidinium Salts, Koichiro Kase, Mitsuyoshi Katayama, Takashi Ishihara, Hiroki Yamanaka, John T. Gupton
Efficient And General Synthesis Of Novel Β-Polyfluoroalkoxy Vinamidinium Salts, Koichiro Kase, Mitsuyoshi Katayama, Takashi Ishihara, Hiroki Yamanaka, John T. Gupton
Chemistry Faculty Publications
Novel β-polyfluoroalkoxy vinamidinium salts 3 and/or 4 were synthesized in good yields by the reaction of N-(2- polyfluoroalkoxy-3 ,3-difluoro-1-propenyI)trimethylammonium iodides (2), prepared from N-(2,3,3-trifluoro-1-propenyl)trimethylammonium iodide (1), with secondary amines in MeCN at 70 °C for 1 h. The salts were also obtainable in comparable yields by the one-pot reaction of 1 with sodium polyfluoroalkoxide followed by treatment with amines.