Results 81 to 90 of about 160 (120)

New Generalized Cyclotomy and Its Applications

Finite Fields and Their Applications, 1998
Let \(n\geq 2\) be a positive integer and \(D_0\) a multiplicative subgroup of \(\mathbb{Z}^*_n\) (integer \(\text{mod }n\), coprime to \(n\)) of index \(d\). Let \(D_j= g_jD_0\), \(j= 1,2,\dots, d-1\). We call \(D_j\) the generalized cyclotomic classes of order \(d\) when \(n\) is composite and the classical cyclotomic classes of order \(d\) when \(n\)
Tor Helleseth
exaly   +3 more sources

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Cyclotomy and the heptadecagon

The Mathematical Gazette, 2016
Cyclotomy is concerned with the division of a circle into a given number of equal segments, amounting to the construction of a regular polygon, say a q-gon, so that we need to deliver the angle α = 2π / q, or the length cos α. The construction is by Euclidean means, which make use of only ruler and compasses.
openaire   +1 more source

Multiple polylogarithms, cyclotomy and modular complexes [PDF]

Mathematical Research Letters, 1998
This is a copy of the article published in Math Res. Letters 5, (1998) 497-516.
A B Goncharov
exaly   +4 more sources

Designs from cyclotomy

1976
In this note we use the theory of cyclotomy to help us construct initial blocks from which we can develop balanced and partially balanced incomplete block designs. Our main construction method, using unions of cyclotomic classes, gives us upper bounds on m, the number of associate classes of the design, but not exact values for m; we discuss the ...
Morgan, Elizabeth J, Street, Anne P, Seberry, Jennifer   +2 more
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Cyclotomy and its application to duadic codes

Finite Fields and Their Applications, 2010
To begin with, the paper defines generalized cyclotomic numbers and describe some elementary properties. Thereafter, `duadic codes' and `cyclotomic duadic codes' have been defined and the authors study some orbit decomposition of \(\mathbb{F}^x_p\). After recalling the higher reciprocity law for polynomial, the authors prove the conjecture of Ding and ...
Hideki Tada, Shigeto Nishimura, Toyokazu Hiramatsu   +2 more
exaly   +4 more sources

Covering arrays from cyclotomy

Designs, Codes and Cryptography, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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New D-optimal designs via cyclotomy and generalised cyclotomy

Australas. J Comb., 1997
Summary: \(D\)-optimal designs are \(n\times n\pm 1\)-matrices where \(n\equiv 2\bmod 4\) with maximum determinant. \(D\)-optimal designs obtained via circulant matrices are equivalent to \(2-\{v;k_1; k_2;k_1+ k_2- {1\over 2} (v-1)\}\) supplementary difference sets, where \(v= {n\over 2}\). We use cyclotomy to construct \(D\)-optimal designs, where \(v\
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Division of the circle (Cyclotomy)

1991
Section 7 of the Disquisitiones arithmeticae deals with division of the circle. We shall give a detailed presentation of the main result, which played an important role in Gauss’s personal development (Sect. 1.1) as well as in the development of algebra.
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Code Synchronization, Cyclotomy, and Finite Geometry

2006 IEEE Information Theory Workshop, 2006
The paper surveys some recent combinatorial constructions of optimal comma-free codes being cosets of linear codes that explore cyclotomy and partitions of hyperplanes or complements of hyperplanes in a finite projective geometry.
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New Classes of Asymptotically Optimal Spectrally-Constrained Sequences Derived from Cyclotomy

Advances in Mathematics of Communications, 2022
Zhengchun Zhou, Zhifan Ye
exaly