منابع مشابه
On cyclotomic cosets and code constructions
New properties of q-ary cyclotomic cosets modulo n = qm − 1, where q ≥ 3 is a prime power, are investigated in this paper. Based on these properties, the dimension as well as bounds for the designed distance of some families of classical cyclic codes can be computed. As an application, new families of nonbinary Calderbank-Shor-Steane (CSS) quantum codes as well as new families of convolutional ...
متن کاملD-Optimal Designs: A Mathematical Programming Approach Using Cyclotomic Cosets
In this paper, a novel approach involving the concepts from mathematical programming and number theory is proposed to find the D-optimal designs. In specific, we will propose a mathematical formulation for the D-optimal design. In addition to that, we will present the use of cyclotomic cosets in the mathematical formulation, in order to reduce the total number of binary variables. We will illus...
متن کاملCyclotomic Units and the Iwasawa Main Conjecture
In these notes, we follow the proof in [1] of the main conjecture of Iwasawa theory making heavy use of the Euler system of cyclotomic units. On the one hand, using the local theory of Coleman series and ideas of Iwasawa one obtains a connection with the p-adic zeta function. On the other hand by CFT and Rubin’s refinement of the ideas of Kolyvagin (and the analytic class number formula) one ob...
متن کاملFamilies of LDPC Codes Derived from Nonprimitive BCH Codes and Cyclotomic Cosets
Low-density parity check (LDPC) codes are an important class of codes with many applications. Two algebraic methods for constructing regular LDPC codes are derived – one based on nonprimitive narrow-sense BCH codes and the other directly based on cyclotomic cosets. The constructed codes have high rates and are free of cycles of length four; consequently, they can be decoded using standard itera...
متن کاملCyclotomic units and Greenberg's conjecture for real quadratic fields
We give new examples of real quadratic fields k for which the Iwasawa invariant λ3(k) and μ3(k) are both zero by calculating cyclotomic units of real cyclic number fields of degree 18.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1977
ISSN: 0097-3165
DOI: 10.1016/0097-3165(77)90070-x