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Minimum weight
About: Minimum weight is a research topic. Over the lifetime, 2002 publications have been published within this topic receiving 28244 citations.
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TL;DR: Assmus--Mattson type theorems for codes and lattices are given and it is shown that a binary doubly even self-dual code of length 24m with minimum weight 4m provides a combinatorial 1-design and an even unimodular lattice of rank 24m that provides a spherical 3-design.
Abstract: In the present paper, we give Assmus–Mattson type theorems for codes and lattices. We show that a binary doubly even self-dual code of length 24m with minimum weight 4m provides a combinatorial 1-design and an even unimodular lattice of rank 24m with minimum norm 2m provides a spherical 3-design. We remark that some of such codes and lattices give t-designs for higher t. As a corollary, we give some restrictions on the weight enumerators of binary doubly even self-dual codes of length 24m with minimum weight 4m. Ternary and quaternary analogues are also given.
7 citations
24 Jun 2007
TL;DR: It is shown that the class of SFA-LDPC codes which are denoted by CA (p, 4) contains a codeword whose minimum weight is 10 or less, if p is a prime number greater than 7 and the Yang's lower bound on the minimum weight of CA ( p,4) is exactly 10.
Abstract: Simple and full-length array LDPC codes (SFA-LDPC codes) is a class of LDPC codes which are algebraically constructed from a family of array codes. The minimum weight of SFA-LDPC codes has been investigated in literatures, but exact minimum weight of the code is not known except for some small parameters. In this paper it is shown that the class of SFA-LDPC codes which are denoted by CA (p, 4) in this paper contains a codeword whose minimum weight is 10 or less, if p is a prime number greater than 7. Combined with the Yang's lower bound on the minimum weight of CA (p,4), this implies that the minimum weight of CA (p, 4) is exactly 10 for any prime p with p > 7.
7 citations
26 Jun 2016
TL;DR: Experimenal results show that the proposed fast heuristic is based on a simple algorithm called “list-heuristic,” which calculates better solutions in shorter time than approximation algorithms for MWVCP.
Abstract: Given a vertex-weighted undirected graph, to find the vertex cover of minimum weight is called minimum weight vertex cover problem (MWVCP). It is known as an NP-hard problem. In this paper, a fast heuristic for MWVCP is proposed. Our algorithm is based on a simple algorithm called “list-heuristic.” Experimenal results show that our algorithm calculates better solutions in shorter time than approximation algorithms for MWVCP.
7 citations
01 Jan 2005
TL;DR: The 6th World Congresses of Structural and Multidisciplinary Optimization (WCOMO) was held in Brazil from 30 May - 03 June 2005 as discussed by the authors, 30 May-03 June 2005.
Abstract: 6th World Congresses of Structural and Multidisciplinary Optimization, Rio de Janeiro, 30 May - 03 June 2005, Brazil
7 citations
Proceedings Article•
01 Dec 19947 citations