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New Binary Linear Codes
"... In this paper, nineteen new binary linear codes are presented which improve the bounds on the maximum possible minimum distance. These codes belong to the class of quasicyclic (QC) codes, and have been constructed using a stochastic optimization algorithm, tabu search. Six of the new codes meet the ..."
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In this paper, nineteen new binary linear codes are presented which improve the bounds on the maximum possible minimum distance. These codes belong to the class of quasicyclic (QC) codes, and have been constructed using a stochastic optimization algorithm, tabu search. Six of the new codes meet
Using linear programming to decode binary linear codes
 IEEE TRANS. INFORM. THEORY
, 2005
"... A new method is given for performing approximate maximumlikelihood (ML) decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel. The decoding algorithm is based on a linear programming (LP) relaxation that is defined by a factor grap ..."
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Cited by 184 (10 self)
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A new method is given for performing approximate maximumlikelihood (ML) decoding of an arbitrary binary linear code based on observations received from any discrete memoryless symmetric channel. The decoding algorithm is based on a linear programming (LP) relaxation that is defined by a factor
On Correctable Errors of Binary Linear Codes
, 2010
"... The error correction capability of binary linear codes with minimum distance decoding, in particular the number of correctable/uncorrectable errors, is investigated for general linear codes and the firstorder Reed–Muller codes. For linear codes, a lower bound on the number of uncorrectable errors ..."
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The error correction capability of binary linear codes with minimum distance decoding, in particular the number of correctable/uncorrectable errors, is investigated for general linear codes and the firstorder Reed–Muller codes. For linear codes, a lower bound on the number of uncorrectable errors
DERIVED FORMS AND BINARY LINEAR CODES
"... Abstract. Derived forms defined by M. Aschbacher in [1] are closely related to combinatorial polarization introduced by H. N. Ward in [6]. A binary linear code is said to be of (divisibility) level r, if r is the biggest integer such that 2 r divides the weight of each codeword. In this paper, we st ..."
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Abstract. Derived forms defined by M. Aschbacher in [1] are closely related to combinatorial polarization introduced by H. N. Ward in [6]. A binary linear code is said to be of (divisibility) level r, if r is the biggest integer such that 2 r divides the weight of each codeword. In this paper, we
On the Convex Geometry of Binary Linear Codes
"... A code polytope is defined to be the convex hull in R n of the points in {0, 1} n corresponding to the codewords of a binary linear code. This paper contains a collection of results concerning the structure of such code polytopes. A survey of known results on the dimension and the minimal polyhedr ..."
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Cited by 1 (0 self)
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A code polytope is defined to be the convex hull in R n of the points in {0, 1} n corresponding to the codewords of a binary linear code. This paper contains a collection of results concerning the structure of such code polytopes. A survey of known results on the dimension and the minimal
Projections of Binary Linear Codes onto Larger Fields
, 2003
"... We study certain projections of binary linear codes onto larger fields. These projections include the wellknown projection of the extended Golay [24, 12, 8] code onto the Hexacode over GF(4) and the projection of the ReedMuller code R(2, 5) onto the unique selfdual [8, 4, 4] code over GF(4). We g ..."
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Cited by 4 (1 self)
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We study certain projections of binary linear codes onto larger fields. These projections include the wellknown projection of the extended Golay [24, 12, 8] code onto the Hexacode over GF(4) and the projection of the ReedMuller code R(2, 5) onto the unique selfdual [8, 4, 4] code over GF(4). We
Edge Local Complementation and Equivalence of Binary Linear Codes
 DESIGNS, CODES AND CRYPTOGRAPHY
"... Orbits of graphs under the operation edge local complementation (ELC) are defined. We show that the ELC orbit of a bipartite graph corresponds to the equivalence class of a binary linear code. The information sets and the minimum distance of a code can be derived from the corresponding ELC orbit. By ..."
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Cited by 17 (9 self)
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Orbits of graphs under the operation edge local complementation (ELC) are defined. We show that the ELC orbit of a bipartite graph corresponds to the equivalence class of a binary linear code. The information sets and the minimum distance of a code can be derived from the corresponding ELC orbit
New binary linear codes from algebraic curves,” Information Theory
 IEEE Transactions on
, 2002
"... Title New binary linear codes from algebraic curves ..."
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Cited by 1 (0 self)
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Title New binary linear codes from algebraic curves
On Weight Distribution for Euclidean Image of Binary Linear Codes
"... Some properties of weight distribution for the Euclidean image of binary linear codes are investigated. Many codes defined on Euclidean space can be regarded as the image of binary linear code with a mapping (from binary to signal constellation). We first show the duality of weight distribution for ..."
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Some properties of weight distribution for the Euclidean image of binary linear codes are investigated. Many codes defined on Euclidean space can be regarded as the image of binary linear code with a mapping (from binary to signal constellation). We first show the duality of weight distribution
On the pseudocodeword redundancy of binary linear codes
 AUTHORS’ BIOGRAPHICAL SKETCHES
, 2012
"... ar ..."
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