| 1. |
- Heden, Olof, et al.
(författare)
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On linear equivalence and phelps codes
- 2010
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Ingår i: Advances in Mathematics of Communications. - : American Institute of Mathematical Sciences (AIMS). - 1930-5346 .- 1930-5338. ; 4:1, s. 69-81
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that all non-full-rank FRH-codes, a class of perfect codes we define in this paper, are linearly equivalent to perfect codes obtainable by Phelps' construction. Moreover, it is shown by an example that the class of perfect FRH-codes also contains perfect codes that are not obtainable by Phelps construction.
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| 2. |
- Heden, Olof, et al.
(författare)
-
On the classification of perfect codes : Extended side class structures
- 2010
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Ingår i: Discrete Mathematics. - Amsterdam, Netherlands : Elsevier. - 0012-365X .- 1872-681X. ; 310:1, s. 43-55
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Tidskriftsartikel (refereegranskat)abstract
- The two 1-error correcting perfect binary codes, C and C′ are said to be equivalent if there exists a permutation π of the set of the n coordinate positions and a word such that . Hessler defined C and C′ to be linearly equivalent if there exists a non-singular linear map φ such that C′=φ(C). Two perfect codes C and C′ of length n will be defined to be extended equivalent if there exists a non-singular linear map φ and a word such thatHeden and Hessler, associated with each linear equivalence class an invariant LC and this invariant was shown to be a subspace of the kernel of some perfect code. It is shown here that, in the case of extended equivalence, the corresponding invariant will be the extension of the code LC.This fact will be used to give, in some particular cases, a complete enumeration of all extended equivalence classes of perfect codes.
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| 3. |
- Hessler, Martin, et al.
(författare)
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Edge cover and polymatroid flow problems
- 2010
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Ingår i: Electronic Journal of Probability. - : Institute of Mathematical Statistics. - 1083-6489. ; 15, s. 2200-2219
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Tidskriftsartikel (refereegranskat)abstract
- In an n by n complete bipartite graph with independent exponentially distributed edge costs, we ask for the minimum total cost of a set of edges of which each vertex is incident to at least one. This so-called minimum edge cover problem is a relaxation of perfect matching. We show that the large n limit cost of the minimum edge cover is W(1)(2) + 2W(1) approximate to 1.456, where W is the Lambert W-function. In particular this means that the minimum edge cover is essentially cheaper than the minimum perfect matching, whose limit cost is pi(2)/6 approximate to 1.645. We obtain this result through a generalization of the perfect matching problem to a setting where we impose a (poly-)matroid structure on the two vertex-sets of the graph, and ask for an edge set of prescribed size connecting independent sets.
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