An Improvement to the Achievement of the Griesmer Bound

We denoted by nq(k, d), the smallest value of n for which an [n, k, d]q code exists for given q, k, d. Since nq(k, d) = gq(k, d) for all d ≥ dk + 1 for q ≥ k ≥ 3, it is a natural question whether the Griesmer bound is attained or not for d = dk , where gq(k, d) = ∑[d/q^i], i=0,...,k-1, dk = (k − 2)q^(k−1) − (k − 1)q^(k−2). It was shown by Dodunekov [2] and Maruta [9], [10] that there is no [gq(k, dk ), k, dk ]q code for q ≥ k, k = 3, 4, 5 and for q ≥ 2k − 3, k ≥ 6. The purpose of this paper is to determine nq(k, d) for d = dk as nq(k, d) = gq(k, d) + 1 for q ≥ k with 3 ≤ k ≤ 8 except for (k, q) = (7, 7), (8, 8), (8, 9).* This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 20540129

Note on an Improvement of the Griesmer Bound for q-ary Linear Codes

Let nq(k, d) denote the smallest value of n for which an [n, k, d]q code exists for given integers k and d with k ≥ 3, 1 ≤ d ≤ q^(k−1) and a prime or a prime power q. The purpose of this note is to show that there exists a series of the functions h3,q, h4,q, ..., hk,q such that nq(k, d) can be expressed.This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 20540129

Construction of Optimal Linear Codes Using Flats and Spreads in a Finite Projective Geometry

In this paper, we shall consider a problem of constructing an optimal linear code whose code length n is minimum among (*, k, d ; s)-codes for given integers k, d and s. In [5], we showed that this problem is equivalent to Problem B of a linear programming which has some geometrical structure and gave a geometrical method of constructing a solution of Problem B using a set of flats in a finite projective geometry and obtained a necessary and sufficient conditions for integers k, d and s that there exists such a geometrical solution of Problem B for given integers k, d and s. But there was no space to give the proof of the main theorem 4.2 in [5]. The purpose of this paper is to give the proof of [5, Theorem 4.2], i.e. to give a systematic method of constructing a solution of Problem B using flats and spreads in a finite projective geometry

A Characterization of Some Minihypers in a Finite Projective Geometry PG(t, 4)

Recently, Hamada and Deza [8] gave a complete characterization of all {vα + 1 + vβ + 1 + vγ + 1, vα + vβ + vγ; t, q}-minihypers for any integers α, β, γ, t and any prime power q such that q ⩾ 5 and either 0 ⩽ α = β < γ < t or 0 ⩽ α < β = γ < t where vl = (ql− 1)/(q − 1) for any integer l ⩾ 0. The purpose of this paper is to characterize all {vα + 1 + vβ + 1 + vγ + 1, vα + vβ + vγ; t, q}-minihypers for any integers t, q, α, β and γ such that q = 4 and either (a) 0 ⩽ α < β = γ < t or (b) 0 ⩽ α = β < γ < t and γ ≠ α + 1. Using those results, all (n, k, d ; 4)-codes meeting the Griesmer bound are characterized for the case k ⩾ 3 and d = 4k−1 − 4α − 4β − 4γ

A Necessary and Sufficient Condition for the Existence of an (n,r)-arc in PG(2,q) and Its Applications

ACM Computing Classification System (1998): E.4.Let q be a prime or a prime power ≥ 3. The purpose of this paper is to give a necessary and sufficient condition for the existence of an (n, r)-arc in PG(2, q ) for given integers n, r and q using the geometric structure of points and lines in PG(2, q ) for n > r ≥ 3. Using the geometric method and a computer, it is shown that there exists no (34, 3) arc in PG(2, 17), equivalently, there exists no [34, 3, 31] 17 code.This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 24540138

イオン液体含有レジン添加型グラスアイオノマーセメントの通電によるせん断接着強度低下 : オンデマンド剥離可能な歯科用スマートセメントのコンセプトと実証

With improvement of bonding strength of recent dental cement, it is difficult nowadays to remove restorations without excessive force or vibration to tooth, occasionally resulting in damage of dentin, enamel, and dental root. Therefore, “smart” dental cement indicating strong bonding and easy debonding-on-demand simultaneously is required. In this research, resin-modified glass-ionomer-cement containing an ionic-liquid, tris(2-hydroxyethyl)methylammonium methylsulfate was produced, and the shear bonding strength before and after direct current application were evaluated. The prototype cement containing 15 to 20 mass% ionic-liquid indicated simultaneously no significant reduction of shear bonding strength from that of the original cement not containing ionic-liquid, and significant reduction of bonding strength to approximately 20% of that of the original cement after direct current application of more than 2 mmC/mm2. The prototype cement in this research demonstrated that the concept of smart dental cement electrically debonding-on-demand is feasible

Cytoskeletal elements in an acoelomorph worm, Praesagittifera naikaiensis

Acoel flatworms can move in a variety of ways such as muscular and ciliary movements via cytoskeletal elements and their neural regulations. However, those locomotive mechanisms have not yet been fully elucidated. In this study, we examined the distribution of cytoskeletal elements including filamentous actin (F-actin) and tubulin, and the neuroanatomical organization in an acoelomorph worm, Praesagittifera naikaiensis (P. naikaiensis). Video microscopy revealed the elongation/contraction and the bending/rotation processes, and the ciliary gliding movement of P. naikaiensis. Histochemical and morphological analysis demonstrated that F-actin networks of inner longitudinal and outer circular muscle fibers were positioned along the entire surface of the body, and that the average distance between the circular muscle fibers in the contracted organism was decreased in the anterior region compared with that in the elongated organism. Electron microscopy showed dense bodies on the muscle cells of P. naikaiensis, which indicates that those muscle cells have the appearance of vertebrate smooth muscle cells. Immunohistochemical analysis revealed that -tubulin-positive signals on the ciliary microtubules had close contact with the F-actin network, and that neurite bundles labelled with anti dSap47 antibody as a neuronal marker run along the anterior-posterior body axis. These results indicate that the well-organized cytoskeletal elements and their neural control systems are preserved in P. naikaiensis, and that their mechanisms involved in those regulation systems are similar to those vertebrate systems. Further studies are needed to clarify the physiological mechanisms underlying the muscular and ciliary movements in P. naikaiensis

レジン添加型グラスアイオノマーセメントの通電後の剪断強度減少に対するイオン液体含有の有無と水中浸漬の影響

The enhancement in the bonding strength of advanced dental cements has enabled long-lasting dental restorations. However, the high bonding strength can cause difficulty in removing these restorations. Therefore, “smart” dental cements with simultaneous strong bonding and easy on-demand debonding ability are required. A resin-modified glass-ionomer-cement (RMGIC) with an ionic liquid (IL) has demonstrated significant reduction in the bonding strength with current application (CA). This research investigates the effects of immersion in distilled water on the electric conductivity and bonding strength of RMGIC with and without an IL and CA. The RMGIC without the IL exhibited significant electric conductivity after immersion, and a significant decrease in bonding strength with CA. In comparison, the electric conductivity after immersion and the decrease in bonding strength with CA were greater for RMGIC with the IL. Thus, the feasibility of smart dental cements capable of electrically debonding-on-demand is indicated

レジン添加型グラスアイオノマーセメントの電気伝導度と通電によるせん断試験強度低下に塩化ナトリウム溶液浸漬が与える影響

Advancements in dental cements have considerably improved their bond strengths. However, high bond strength often makes the removal of restorations difficult. Thus, smart dental cements that show controllable bond strength are required. A conventional resin-modified glass-ionomer-cement demonstrated a significant reduction in the bond strength after current application. However, for this system, the ions in the cement are released into the oral cavity, resulting in a reduction of the electrical conductivity and in losses of the expected on-demand debonding property. Herein, the effects of immersion in 0.9 and 15% NaCl solutions on the electrical conductivity and debonding properties were investigated. The cement immersed in 0.9% NaCl solution from 1 to 28 days maintained similar bond strength reductions after current application, whereas that in 15% NaCl solution initially showed no bond strength reduction after 1 day but exhibited an increase in the bond strength reduction after immersion for 28 days