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* Correspondence: taekyun64@hotmail.com Department of Mathematics, Kwangwoon University, Seoul 139701, Republic of Korea Full list of author information is available at the end of the article Abstract Let Pn be the space of polynomials of degree less than or equal to n. In this article, using the Bernoulli basis {B0(x), . . . , Bn(x)} for Pn consisting of(More)
In this paper, a home network message specification for white goods based on power line communication is proposed. It is designed for white goods such as air conditioners, refrigerators, washing machines, etc. The proposed home network message specification is composed of a virtual device service and a devicespecific attribute. For practical implementation,(More)
Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z N ∪ {0}. The p-adic absolute value on Cp is normalized so that |p|p 1/p. Assume that q ∈ Cp(More)
Let P = n11 ⊕ · · · ⊕ nt1 be the poset given by the ordinal sum of the antichains ni1 with ni elements. We derive MacWilliams-type identities for the fragment and sphere enumerators, relating enumerators for the dual C of the linear code C on P and those for C on the dual poset P̌. The linear changes of variables appearing in the identities are explicit. So(More)
We derive eight basic identities of symmetry in three variables related to Euler polynomials and alternating power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in two variables. These abundances of symmetries shed new light even on the existing identities so as to yield some further(More)
Let P = n11 ⊕ · · · ⊕ nt1 be the poset given by the ordinal sum of the antichains ni1 with ni elements. Then we consider the P-weight enumerator for the linear code C of length n (n = n1 + · · · + nt) over Fq on P, and derive a MacWilliams-type identity relating the weight enumerator for the dual code C⊥ of C on P and that for C on the dual poset 5 P of P.(More)
In this paper, we derive eight basic identities of symmetry in three variables related to q-Euler polynomials and the q -analogue of alternating power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in two variables. These abundance of symmetries shed new light even on the existing(More)