arXiv subjects
Publications and source records attributed to Dae San Kim.
In this paper, we study umbral calculus to have alternative ways of obtaining our results. That is, we derive some interesting identities of the higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus to have alternative ways.
In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.
Recently, D. S. Kim and T. Kim have studied applications of um- bral calculus associated with p-adic invariant integrals on Zp (see [6]). In this paper, we investigate some interesting properties arising from umbral calculus. These properties are useful in deriving some identities of Bernoulli polynomials.
In this paper, we study some properties of umbral calculus related to Appell sequence. From those properties, we derive new and interesting identities of Frobenius-Euler polynomials.
In this paper we study some properties of the fermionic p-adic integrals on Zp arising from the umbral calculus
In this paper, we study some properties of Euler polynomials arising from umbral calculus. Finally, we give some interesting identities of Euler polynomials using our results. Recently, Dere and Simsek have studied umbral calculus related to special polynomials (see[6]).
In this paper, we give some new and interesting identities which are derived from the basis of Frobenius-Euler. Recently, Simsek et als(see [13]) have given some identities of q-analogue of Frobenius-Euler polynomials related to q-Bernstein polynomials. From the methods of our paper, we can also derive the results and identities of Simsek et als (cf.[13]).
In this paper, we study some properties of associated sequaences in umbral calculus. From these properties, we derive new and interesting identities of several kinds of polynomials.
The purpose of this paper is to present a syatemic study of some familes of higher-order Euler numbers and polynomials. In particular, by using the basis property of higher-order Euler polynomials for the space of polynomials of degree less than and equal to n, we derive some interesting identities for the higher-order Euler polynomias.
In this paper, we derive some new and interesting idebtities for Bernoulli, Euler and Hermite polynomials associated with Chebyshev polynomials.
In this paper we derive some interesting identities arising from the orhtogonality of gegenbauer polynomials.
We construct a binary linear code $C(O(3,q))$, associated with the orthogonal group $O(3,q)$. Here $q$ is a power of two. Then we obtain a recursive formula for the odd power moments of Kloosterman sums with trace one arguments in terms of the frequencies of weights in the codes $C(O(3,q))$ and $C(Sp(2,q))$. This is done via Pless power moment identity and by utilizing the explicit expressions of Gauss sums for the orthogonal groups.
Translation association schemes are constructed from actions of finite groups on finite abelian groups satisfying certain natural conditions. It is also shown that the mere existence of maps from finite groups to themselves sending each element in their groups to its `adjoint' entails the self-duality of the constructed association schemes. Many examples of these, including Hamming scheme and sesquilinear forms schemes, are provided. This con- struction is further generalized to show the duality of the association schemes coming from actions of two finite groups on the same finite abelian group. An example of this is supplied with weak Hamming schemes.
In this paper, we construct two ternary linear codes associated with the symplectic groups Sp(2,q) and Sp(4,q). Here q is a power of three. Then we obtain recursive formulas for the power moments of Kloosterman sums with square arguments and for the even power moments of those in terms of the frequencies of weights in the codes. This is done via Pless power moment identity and by utilizing the explicit expressions of "Gauss sums" for the symplectic groups Sp(2n,q).
In 1991, Wei introduced generalized minimum Hamming weights for linear codes and showed their monotonicity and duality. Recently, several authors extended these results to the case of generalized minimum poset weights by using different methods. Here, we would like to prove the duality by using matroid theory. This gives yet another and very simple proof of it. In particular, our argument will make it clear that the duality follows from the well-known relation between the rank function and the corank function of a matroid. In addition, we derive the weight distributions of linear MDS and Near-MDS poset codes in the same spirit.
Let $q$ be any prime power and let $d$ be a positive integer greater than 1. In this paper, we construct a family of $M$-ary sequences of period $q-1$ from a given $M$-ary, with $M|q-1$, Sidelikov sequence of period $q^d-1$. Under mild restrictions on $d$, we show that the maximum correlation magnitude of the family is upper bounded by $(2d -1) \sqrt { q }+1$ and the asymptotic size, as $q\rightarrow \infty$, of that is $\frac{ (M-1)q^{d-1}}{d }$. This extends the pioneering work of Yu and Gong for $d=2$ case.