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11.
In this paper it is shown that the weight enumerator of a bordered double circulant self-dual code can be obtained from those of a pure double circulant self-dual code and its shadow through a relationship between bordered and pure double circulant codes. As applications, a restriction on the weight enumerators of some extremal double circulant codes is determined and a uniqueness proof of extremal double circulant self-dual codes of length 46 is given. New extremal singly-even [44,22,8] double circulant codes are constructed. These codes have weight enumerators for which extremal codes were not previously known to exist. 相似文献
12.
13.
14.
In this paper, double circulant self-dual codes over GF(7) are presented, including [12,6,6] codes which are new optimal codes. It is shown that the supports of the codewords of
weights 9, 10 and 11 in double circulant [20,10,9] codes form 3-designs. For larger lengths, some good self-dual codes are
constructed from weighing matrices.
Received: June 24, 1996 / Revised: February 28, 1997 相似文献
15.
16.
Steven T. Dougherty T. Aaron. Gulliver Manabu Oura 《Designs, Codes and Cryptography》2006,38(1):97-112
We study higher weights applied to ternary and quaternary self-dual codes. We give lower bounds on the second higher weight
and compute the second higher weights for optimal codes of length less than 24. We relate the joint weight enumerator with
the higher weight enumerator and use this relationship to produce Gleason theorems. Graded rings of the higher weight enumerators
are also determined.
This work was supported in part by Northern Advancement Center for Science & Technology and the Natural Sciences and Engineering
Research Council of Canada. 相似文献
17.
For a domainU on a certaink-dimensional minimal submanifold ofS
n orH
n, we introduce a “modified volume”M(U) ofU and obtain an optimal isoperimetric inequality forU k
k
ω
k
M (D)
k-1
≤Vol(∂D)
k
, where ω
k
is the volume of the unit ball ofR
k
. Also, we prove that ifD is any domain on a minimal surface inS
+
n
(orH
n, respectively), thenD satisfies an isoperimetric inequality2π A≤L
2+A2 (2π A≤L2−A2 respectively). Moreover, we show that ifU is ak-dimensional minimal submanifold ofH
n, then(k−1) Vol(U)≤Vol(∂U).
Supported in part by KME and GARC 相似文献
18.
Usher AJ Lucas NT Dalton GT Randles MD Viau L Humphrey MG Petrie S Stranger R Willis AC Rae AD 《Inorganic chemistry》2006,45(26):10859-10872
Reactions of the tetrahedral clusters MoIr3(mu-CO)3(CO)8(eta-L) (L = C5HMe4, C5Me5) with the carbonylmetalate anions [Mo(CO)3(eta-L)]- afford the trigonal bipyramidal clusters Mo2Ir3(mu3-H)(mu-CO)2(CO)9(eta-L)2 (L = C5HMe4 (3c), 74%; L = C5Me5 (3d), 55%) in which the group 6 metal atoms occupy the apexes; reaction of the cyclopentadienylmolybdenum-containing analogues or their cyclopentadienyltungsten-containing homologues failed to afford analogous products. Reactions of MIr3(mu-CO)3(CO)8(eta-C5H5) (M = Mo, W) with [M(CO)3(eta-L)]- (L = C5HMe4, C5Me5) afford the core-expanded heteroapex clusters M2Ir3(mu3-H)(mu-CO)2(CO)9(eta-C5H5)(eta-L) (M = Mo, L = C5HMe4 (5c), 9%, L = C5Me5 (5d), 4%; M = W, L = C5Me5 (6d), 5%) in low yield, together with the homoapex clusters M2Ir3(mu3-H)(mu-CO)2(CO)9(eta-L)2 (M = Mo, L = C5HMe4 (3c), 81%, L = C5Me5 (3d), 60%; M = W, L = C5Me5 (4d), 5%) in much higher yield for the Mo-containing examples. The identities of clusters 3c,d, 4d, and 5c,d have been confirmed by single-crystal X-ray diffraction studies, with the same disposition of ligands about the trigonal bipyramidal cluster cores being observed in each case, a ligand arrangement that has been examined by complementary density functional theory studies. While cluster 5d is accessible as above, no reaction is observed from MoIr3(mu-CO)3(CO)8(eta-C5Me5) and [M(CO)3(eta-C5H5)]-. Treating MoIr3(mu-CO)3(CO)8(eta-C5H5) with 1 equiv of [M(CO)3(eta-C5Me5)]- affords 5d as the major product, a further 1 equiv affording some MoIr3(mu-CO)3(CO)8(eta-C5Me5) and a third 1 equiv giving a good yield of 3d. This is consistent with reaction proceeding by apex fragment addition, followed by apex fragment elimination, and finally a further apex fragment addition, the homometallic incoming apexes being distinguished from the departing vertices by their highly methylated cyclopentadienyl ligands. Spectroscopic data suggest that the electron density at these disparate-metal-containing cluster cores is tunable by progressive (conceptual) cyclopentadienyl alkylation. 相似文献
19.
For a given boundary Γ in Rn consisting of arcs and vertices, with two or more arcs meeting at each vertex, we treat the problem of estimating the area
density of a soap film-like surface Σ spanning Γ. Σ is assumed locally to minimize area, or more generally, to be strongly
stationary for area with respect to Γ. We introduce a notion of total curvature (Γ) for such graphs, or nets, Γ. We show that 2π times the area density of Σ at any point is less than or equal to (Γ). For n=3, these density estimates imply, for example, that if (Γ)≤3.649π, then the only possible singularities of a piecewise smooth (M,0,δ)-minimizing set Σ are curves, along which three smooth sheets of Σ meet with equal angles of 120°.
Second author supported in part by NSF grant 00-71862. 相似文献
20.
In this paper we give the structure of constacyclic codes over formal power series and chain rings. We also present necessary and sufficient conditions on the existence of MDS codes over principal ideal rings. These results allow for the construction of infinite families of MDS self-dual codes over finite chain rings, formal power series and principal ideal rings. We also define the Reed–Solomon codes over principal ideal rings. 相似文献