相关论文: Variations on the Fibonacci Universal Code
We explain the use of category theory in describing certain sorts of anyons. Yoneda's lemma leads to a simplification of that description. For the particular case of Fibonacci anyons, we also exhibit some calculations that seem to be known…
This document is a companion to the paper "Monk's Rule and Giambelli's Formula for Peterson Varieties of All Lie Types." We provide the source code for computing the Giambelli's formula in types $E_6$ $E_7$ and $E_8$.
This report is devoted to introduction in multichannel algorithm based on generalized numeration notations (GPN). The internal, external and mixed account are entered. The concept of the GPN and its classification as decomposition of an…
We define Convolutional Goppa Codes over algebraic curves and construct their corresponding dual codes. Examples over the projective line and over elliptic curves are described, obtaining in particular some Maximum-Distance Separable (MDS)…
Fibonacci numbers and the golden ratio can be found in nearly all domains of Science, appearing when self-organization processes are at play and/or expressing minimum energy configurations. Several non-exhaustive examples are given in…
A new approach to joint source-channel coding is presented in the context of communicating correlated sources over multiple access channels. Similar to the separation architecture, the joint source-channel coding system architecture in this…
In this article we study a generalization of Fibonomials, replacing the Fibonacci sequences by bivariate s-Fibonacci polynomial sequences. We call the obtained objects "Bivariate s-Fibopolynomials".
We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than 2 states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional…
We present a nonlocal construction of universal gates by means of holonomic (geometric) quantum teleportation. The effect of the errors from imperfect control of the classical parameters, the looping variation of which builds up holonomic…
Separating codes have their applications in collusion-secure fingerprinting for generic digital data, while they are also related to the other structures including hash family, intersection code and group testing. In this paper we study…
We present a differential-calculus-based method which allows one to derive more identities from {\it any} given Fibonacci-Lucas identity containing a finite number of terms and having at least one free index. The method has two {\it…
Recent results about sums of cubes of Fibonacci numbers [Frontczak, 2018] are extended to arbitrary powers.
We consider various properties and manifestations of some sign-alternating univariate polynomials borne of right-triangular integer arrays related to certain generalizations of the Fibonacci sequence. Using a theory of the root geometry of…
In part 1 of this paper some linear weighted generalized Fibonacci number summation identities were derived using the fact that the Fibonacci number is the residue of a rational function. In this part, using the same method, some quadratic…
Adaptive coding faces the following problem: given a collection of source classes such that each class in the collection has non-trivial minimax redundancy rate, can we design a single code which is asymptotically minimax over each class in…
The standard approach to the design of individual space-time codes is based on optimizing diversity and coding gains. This geometric approach leads to remarkable examples, such as perfect space-time block codes, for which the complexity of…
The breakthrough of achieving fully homomorphic encryption sparked enormous studies on where and how to apply homomorphic encryption schemes so that operations can be performed on encrypted data without the secret key while still obtaining…
In addition to their applications in data storage, communications systems, and consumer electronics, LCD codes -- a class of linear codes -- have been employed in cryptography recently. LCD cyclic codes were referred to as reversible cyclic…
In communication through asymmetric channels the capacity-achieving input distribution is not uniform in general. Homophonic coding is a framework to invertibly convert a (usually uniform) message into a sequence with some target…
In two previous papers we have presented partition formulae for the Fibonacci numbers motivated by the appearance of the Fibonacci numbers in the representation theory of the 3-Kronecker quiver and its universal cover, the 3-regular tree.…