2,531 research outputs found

    Optimal Binary Subspace Codes of Length 6, Constant Dimension 3 and Minimum Distance 4

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    It is shown that the maximum size of a binary subspace code of packet length v=6v=6, minimum subspace distance d=4d=4, and constant dimension k=3k=3 is M=77M=77; in Finite Geometry terms, the maximum number of planes in PG(5,2)\operatorname{PG}(5,2) mutually intersecting in at most a point is 7777. Optimal binary (v,M,d;k)=(6,77,4;3)(v,M,d;k)=(6,77,4;3) subspace codes are classified into 55 isomorphism types, and a computer-free construction of one isomorphism type is provided. The construction uses both geometry and finite fields theory and generalizes to any qq, yielding a new family of qq-ary (6,q6+2q2+2q+1,4;3)(6,q^6+2q^2+2q+1,4;3) subspace codes

    Johnson type bounds for mixed dimension subspace codes

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    Subspace codes, i.e., sets of subspaces of Fqv\mathbb{F}_q^v, are applied in random linear network coding. Here we give improved upper bounds for their cardinalities based on the Johnson bound for constant dimension codes.Comment: 16 pages, typos correcte

    Classification of large partial plane spreads in PG(6,2)PG(6,2) and related combinatorial objects

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    In this article, the partial plane spreads in PG(6,2)PG(6,2) of maximum possible size 1717 and of size 1616 are classified. Based on this result, we obtain the classification of the following closely related combinatorial objects: Vector space partitions of PG(6,2)PG(6,2) of type (31641)(3^{16} 4^1), binary 3×43\times 4 MRD codes of minimum rank distance 33, and subspace codes with parameters (7,17,6)2(7,17,6)_2 and (7,34,5)2(7,34,5)_2.Comment: 31 pages, 9 table

    Mini-Collagens in Hydra Nematocytes

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    We have isolated and characterized four collagen-related c-DNA clones (N-COL 1, N-COL 2, N-COL 3, N-COL 4) that are highly expressed in developing nematocytes in hydra. All four c-DNAs as well as their corresponding transcripts are small in size (600-1,000 bp). The deduced amino acid sequences show that they contain a central region consisting of 14 to 16 Gly-X-Y triplets. This region is flanked amino-terminal by a stretch of 14-23 proline residues and carboxy-terminal by a stretch of 6-9 prolines. At the NH2- and COOH-termini are repeated patterns of cysteine residues that are highly conserved between the molecules. A model is proposed which consists of a central stable collagen triple helix of 12-14 nm length from which three 9-22 nm long polyproline II type helices emerge at both ends. Disulfide linkage between cysteine- rich segments in these helices could lead to the formation of oligomeric network structures. Electrophoretic characterization of nematocyst extracts allows resolution of small proline-rich polypeptides that correspond in size to the cloned sequences
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