Computer Science Technical Reports
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Recommendations Made Easy
(20140623)Fueled by evergrowing data, the need to provide recommendations for consumers, and the considerable domain knowledge required to implement distributed large scale graph solutions we sought to provide recommendations for ... 
Matrix Representations of GF(p[superscript n]) over GF(p)
(20140131)We show that any nonsingular nxn matrix of order p[superscript n]1 over GF(p) is a generator of a matrix representation of GF(p[superscript n]). We also determine the number of matrix representations of GF(p[superscript ... 
Fields and Cyclic Codes for Error Detection
(20140114)This technical report discusses some of the aspects of error detection using finite fields. 
The Conjugacy Classes of 3x3 and 4x4 Matrices Over GF(2)
(20130920)The general linear groups over GF(2) have an intricate and interesting structure. This report does some preliminary work in examining the structure of two of these groups by giving the conjugacy classes of 3x3 and 4x4 ... 
The Class 10 4x4 Faithful Representations of S4 over GF(2)
(20130920)There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 10. (There is no class 6, so the classes are ... 
Class 9 4x4 Faithful Representations of S4 over GF(2)
(20130920)There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 9. 
The Class 8 4x4 Faithful Representations of S4 over GF(2)
(20130920)There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 8. This class includes the standard representation ... 
The Class 7 4x4 Faithful Representations of S4 over GF(2)
(20130920)There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 7. 
The Class 5 4x4 Faithful Representations of S4 over GF(2)
(20130920)There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 5. 
The Class 4 4x4 Faithful Representations of S4 over GF(2)
(20130920)There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 4. 
The Class 3 4x4 Faithful Representations of S4 over GF(2)
(20130920)There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 3. 
The Class 2 4x4 Faithful Representations of S4 over GF(2)
(20130920)There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 2. 
The Class 1 4x4 Faithful Representations of S4 over GF(2)
(20130920)There are 9 conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices over GF(2). This report lists the representations belonging to class 1. 
The Representations of GF(8) in GL3(2)
(20130920)This report gives one subgroup of each of the conjugacy classes of the subgroups of S7. 
The Representations of GF(8) in GL3(2)
(20130920)As is well known (or should be well known) the finite field GF(2^k) can be represented in the general linear group of kxk matrices over GF(2). There are many such representations. This report gives the 8 representations ... 
The Super Symmetric Representations of S4 in GL3(2)
(20130920)This report gives all conjugacy classes of the super symmetric groups HR3 and VR3 
Primitive Polynomials for the Field GF(3): Degree 2 through Degree 11
(20130920)This report lists the primitive polynomials over GF(3) of degree 2 through 11. These polynomials were generated using a new matrixbased technique I invented. 
Primitive Polynomials for the Field GF(2): Degree 2 through Degree 16
(20130920)This report lists the primitive polynomials over GF(2) of degree 2 through 16. These polynomials were generated using a new matrixbased technique I invented. 
Generator Pairs for all 4x4 GF(2) Representations of S4
(20130920)There are nine conjugacy classes of faithful representations of S4 in the general linear group of 4x4 matrices. This report gives generator matrices for one group in each class. These generator pairs allow each of the ...