• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.547-562
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• 2011

We establish a new formalism of the non-periodic autocorrelation function (NPAF) of two sequences, which is suitable for the computation of the NPAF of any two sequences. It is shown, that this encoding of NPAF is efficient for sequences of small weight. In particular, the check for two sequences of length n having weight w to have zero NPAF can be decided in $O(n+w^2{\log}w)$. For n > w^2{\log}w$, the complexity is O(n) thus we cannot expect asymptotically faster algorithms.

• Journal of Communications and Networks
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• 제14권3호
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• pp.230-236
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• 2012

Based on the known binary sequence sets and Gray mapping, a new method for constructing quaternary sequence sets is presented and the resulting sequence sets' properties are investigated. As three direct applications of the proposed method, when we choose the binary aperiodic, periodic, and Z-complementary sequence sets as the known binary sequence sets, the resultant quaternary sequence sets are the quaternary aperiodic, periodic, and Z-complementary sequence sets, respectively. In comparison with themethod proposed by Jang et al., the new method can cope with either both the aperiodic and periodic cases or both even and odd lengths of sub-sequences, whereas the former is only fit for the periodic case with even length of sub-sequences. As a consequence, by both our and Jang et al.'s methods, an arbitrary binary aperiodic, periodic, or Z-complementary sequence set can be transformed into a quaternary one no matter its length of sub-sequences is odd or even. Finally, a table on the existing quaternary periodic complementary sequence sets is given as well.

• 대한수학회보
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• 제55권3호
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• pp.763-776
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• 2018

In this paper we consider the element-wise (Hadamard) product (or sum) of elliptic divisibility sequences and study the periodic structure of these sequences. We obtain that the element-wise product (or sum) of elliptic divisibility sequences are periodic modulo a prime p like linear recurrence sequences. Then we study periodicity properties of product sequences. We generalize our results to the case of modulo $p^l$ for some prime p > 3 and positive integer l. Finally we consider the p-adic behavior of product sequences and give a generalization of [9, Theorem 4].

• 한국통신학회논문지
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• 제33권1C호
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• pp.6-11
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• 2008

주기 수열에서 각 주기의 임의의 위치에 r개의 심볼을 추가하는 경우, 더 긴 주기를 가지는 수열을 얻을 수 있다. 본 논문에서는 주기 수열에 r개의 심볼을 추가한 수열의 선형복잡도에 대한 기존 결과들을 정리하고 GF(p)상에서 정의된 최대주기 수열에 1개의 심볼을 추가함으로써 얻어지는 수열들의 선형복잡도의 분포를 분석한다. 그리고 이진 최대주기 수열들의 1-심볼 추가 k-오류 선형복잡도에 대한 새로운 사실들을 유도함으로써 수열의 안정성을 평가한다.

• 한국통신학회논문지
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• 제31권9C호
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• pp.846-852
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• 2006

${\kappa}$-오류 선형복잡도는 통신 시스템 및 스트림 암호 시스템 등에 사용되는 수열의 안정성 여부를 판단하는 중요한 척도이다. 본 논문은 p가 소수이고 2가 모듈로 $p^2$의 원시근일 때 $p^m$-주기 이진 수열의 k-오류 선형복잡도와 해당 오류벡터를 효과적으로 구할 수 있는 알고리듬을 소개한다. 또한 암호학적인 관점에서 정의된 ${\kappa}$-오류 선형 복잡도의 의미를 부호 이론의 관점에서 살펴봄으로써 부호어의 길이가 $p^m$인 이진 순환 부호를 효과적으로 복호할 수 있는 알고리듬을 소개하며 이러한 부호의 최소 거리에 관한 중요한 성질들을 유도한다.

• 대한수학회보
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• 제61권2호
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• pp.381-399
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• 2024

In this paper, we introduce a class of Moran measures generated by quasi periodic sequences, and consider power decay of the Fourier transforms of this kind of measures.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권4호
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• pp.253-265
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• 2018

In this paper, we introduce the concept of Fibonacci sequences on MV-algebras and study them accurately. Also, by introducing the concepts of periodic sequences and power-associative MV-algebras, other properties are also obtained. The relation between MV-algebras and Fibonacci sequences is investigated.

• Journal of applied mathematics & informatics
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• 제38권1_2호
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• pp.99-112
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• 2020

The study is about the bounds of the spectral norms of r-circulant and geometric circulant matrices with the sequences called biperiodic Jacobsthal numbers. Then we give bounds for the spectral norms of Kronecker and Hadamard products of these r-circulant matrices and geometric circulant matrices. The eigenvalues and determinant of r-circulant matrices with the bi-periodic Jacobsthal numbers are obtained.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2002년도 ITC-CSCC -3
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• pp.1996-1999
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• 2002

Applying a higher frequency periodic control signal, a state of a chaotic pulse-train generator is quantized. The circuit has various co-existing super-stable periodic pulse-trains (ab. SSPTs) and generates one of them depending on the initial state. Also correlation characteristics of the SSPTs are analyzed precisely. We then consider application of the SSPTs to spread sequences of CDMA with pulse-train signals.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.221-233
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• 2016

The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.