Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Abelian group (2)
- Computer simulation (2)
- Difference set (2)
- 2-groups (1)
- Analytic functions (1)
-
- Animal communication (1)
- Backward shift (1)
- Backward shift operator (1)
- Banach space (1)
- Computer network protocols (1)
- Difference sets (1)
- Discrete Log Cryptosystems (1)
- Elliptic Curve Cryptography (1)
- Error correction (1)
- Frequency division multiplexing (1)
- Golay codes (1)
- Graphs (1)
- Grids (1)
- Hadamard (1)
- Hadamard difference set (1)
- Mathematics (1)
- McFarland (1)
- Nonabelian group (1)
- Out-of-phase periodic autocorrelation coefficients (1)
- Parallel processing (Electronic computers) (1)
- Perfect binary array (1)
- Power control (1)
- Pseudocontinuations (1)
- Quantum Computing (1)
- Reed-Muller codes (1)
- Publication
- Publication Type
Articles 1 - 11 of 11
Full-Text Articles in Entire DC Network
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.
On Some New Constructions Of Difference Sets, Sarah Agnes Spence
On Some New Constructions Of Difference Sets, Sarah Agnes Spence
Honors Theses
Difference sets are mathematical structures which arise in algebra and combinatorics, with applications in coding theory. The fundamental question is when and how one can construct difference sets. This largely expository paper looks at standard construction methods and describes recent findings that resulted in new families of difference sets. This paper provides explicit examples of difference sets that arise from the recent constructions. By gaining a thorough understanding of these new techniques, it may be possible to generalize the results to find additional new families of difference sets. The paper also introduces partial and relative difference sets and discusses how …
On The Automatic Generation Of Network Protocol Simulators, Andrew Chen
On The Automatic Generation Of Network Protocol Simulators, Andrew Chen
Honors Theses
Computers communicate with each other over various communication networks via a language known as a protocol. The design of the protocol can have a significant impact on the efficiency (and effectiveness) of the network. Because building an actual network to test the performance (and reliability) of a new protocol is rather expensive and time consuming, there is an interest in simulating network protocols in order to determine how efficient the communication network is. We are therefore interested in automatically generating simulators that could measure the performance of the new protocols. There are two main parts to this project. The first …
Temporal Flocking And Cacophony Simulating Agent Communication In A Noisy Environment, Jessica R. Crawford
Temporal Flocking And Cacophony Simulating Agent Communication In A Noisy Environment, Jessica R. Crawford
Honors Theses
Realistic communication is one of the most difficult aspects of simulating group behavior because the patterns produced by group communication are complex and not easily definable. In this paper, we present a model, developed using artificial life methodology, for creating simulations of group communication. Our model employs autonomous, artificial agents to produce emergent group behavior that resembles the communication patterns of a group, specifically, a flock of birds. Each agent collects information about its environment and its neighbors and follows a set of rules designed to meet both group goals and individual agent goals. Because we seek to establish emergent …
Parallel Programming, Peter Dailey
Parallel Programming, Peter Dailey
Honors Theses
The speed of technology is always increasing, especially in the field of computing. Unfortunately, the size of the problems needing to be solved are also growing in many areas. In order to keep up with this, parallel computing has become an important research area. The term parallel computing essentially refers to using multiple processors cooperating to solve a problem. For certain problems this can speed up the solution by a factor ofN, the number of processors being used. There are algorithms, for which there is no speed increase due to certain dependencies.
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.
Irreducible K-To-1 Maps Onto Grids, Susan M. Parker
Irreducible K-To-1 Maps Onto Grids, Susan M. Parker
Honors Theses
In this paper we explore the existence of exactly k-to-1 continuous functions between graphs, and more specifically 2-to-1 continuous function between graphs that are irreducibly 2-to-1, meaning that no restriction of the function to a subgraph is 2-to-l. We show how to construct such functions in some general cases, and then more specifically onto rectangular grids. We have in mind an application to distributed networks and signal verification.