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76
On the Trellis Complexity of Certain Binary Linear Block Codes
"... investigated, in the case where the weights of nonzero codewords in g ..."
Minimal codewords in linear codes
 Serdica Math. J
"... The sets of minimal codewords in linear codes were considered for the first time in connection with a decoding algorithm (TaiYang Hwang [2]). Additional interest to them was sparked by a work of J. Massey [3], where it was shown that they describe minimal access structures in secretsharing based o ..."
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Cited by 3 (1 self)
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on linear codes. Definition. Let C be a q−ary linear code. A nonzero codeword c ∈ C is called minimal if its support does not contain the support of any other nonzero codeword as proper subset. It seems to be quit difficult to describe the set of minimal codewords for an arbitrary linear code even
Minimal Codewords and Secret Sharing
 Proceedings of the 6th Joint SwedishRussian International Workshop on Information Theory
, 1993
"... : The use of a linear code to "split" secrets into equalsize shares is considered. The determination of which sets of shares can be used to obtain the secret leads to the apparently new notion of minimal codewords in a linear code. It is shown that the minimal codewords in the dual code c ..."
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Cited by 51 (1 self)
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: The use of a linear code to "split" secrets into equalsize shares is considered. The determination of which sets of shares can be used to obtain the secret leads to the apparently new notion of minimal codewords in a linear code. It is shown that the minimal codewords in the dual code
Bounds on Minimal Codewords in Linear Codes
, 1994
"... The notion of minimal codewords in linear codes was introduced recently by Massey. In this paper two weight bounds on minimal codewords are proved; an upper bound above which no codewords are minimal and a lower bound below which all codewords are minimal. It is shown for Hamming codes that every we ..."
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The notion of minimal codewords in linear codes was introduced recently by Massey. In this paper two weight bounds on minimal codewords are proved; an upper bound above which no codewords are minimal and a lower bound below which all codewords are minimal. It is shown for Hamming codes that every
Minimumweight Codewords for LDPC Codes
, 710
"... Despite the NP hardness of acquiring minimum distance dm for linear codes theoretically, in this paper we propose one experimental method of finding minimumweight codewords, the weight of which is equal to dm for LDPC codes. One existing syndrome decoding method, called serial belief propagation (B ..."
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syndrome changes to allzero state, the lightest error pattern reduces to allzero, the lightest nonzero error pattern is a valid codeword to update lightest codeword list. Given sufficient codewords sending, the survived lightest codewords are likely to be the target. Compared with existing techniques
The Depth Distribution  A New Characterization for Linear Codes
 IEEE Trans. Inform. Theory
, 1997
"... We apply the wellknown operator of sequences, the derivative DDD, on codewords of linear codes. The depth of a codeword c is the c (the derivative applied i consecutive times) is zero. We show that the depth distribution of the nonzero codewords of an [n; k] linear code consists of exactly k non ..."
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We apply the wellknown operator of sequences, the derivative DDD, on codewords of linear codes. The depth of a codeword c is the c (the derivative applied i consecutive times) is zero. We show that the depth distribution of the nonzero codewords of an [n; k] linear code consists of exactly k
Codes Project
, 2013
"... The goal is to design an algorithm to generate tdesigns from the support sets of extended quadratic residue codes. A code C over an alphabet Q is a proper subset of Qn (n is the length of the code). Often Qn is a Qvector space (with Q a field) and the code C is a linear subspace (such a code is ca ..."
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is called a linear code). The elements of C are called codewords. A minimum weight codeword is a nonzero codeword with minimal number of nonzero
Almost all Pauli Channels have nonzero quantum capacities
, 909
"... Quantum transmission rate may be improved by using input of entangled state instead of product state for Pauli channel. Using GHZ state as input for the depolarizing channel (a special Pauli channel), the channel fidelity of nonzero quantum capacity was improved from> 0.81071 to> 0.80944. We ..."
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Quantum transmission rate may be improved by using input of entangled state instead of product state for Pauli channel. Using GHZ state as input for the depolarizing channel (a special Pauli channel), the channel fidelity of nonzero quantum capacity was improved from> 0.81071 to> 0.80944. We
Optimal linear precoders for MIMO wireless correlated channels with nonzero mean in spacetime coded systems
 IEEE TRANS. SIGNAL PROCESSING
, 2006
"... This paper proposes linear precoder designs exploiting statistical channel knowledge at the transmitter in a multipleinput multipleoutput (MIMO) wireless system. The paper focuses on channel statistics, since obtaining realtime channel state information at the transmitter can be difficult due to ..."
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Cited by 31 (4 self)
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error probability (PEP) between a pair of block codewords, averaged over channel fading statistics. Two PEP design criteria are studied—minimum distance and average distance. The optimal precoder with an orthogonal STBC is established, using a convex optimization framework. Different relaxations
Covering arrays and intersecting codes
 JOURNAL OF COMBINATORIAL DESIGNS
, 1993
"... A tcovering array is a set of k binary vectors of length n with the property that, in any t coordinate positions, all 2t possibilities occur at least once. Such arrays are used for example in circuit testing, and one wishes to minimize k for given values of n and t. The case t = 2 was solved by Rkn ..."
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Cited by 43 (0 self)
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nonzero codewords meet). This article studies the properties of 3covering arrays and intersecting codes, and gives a table of the best 3covering arrays presently known. For large n the minimal k satisfies 3.21256 < k / log n < 7.56444. 01993
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