Monotone span program(MSP) and linear code(LC) are efficient tools to construct linear secret sharing scheme(LSSS) for a given access structure. Since the size of an MSP or the length of an LC corresponds to the commu...
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Monotone span program(MSP) and linear code(LC) are efficient tools to construct linear secret sharing scheme(LSSS) for a given access structure. Since the size of an MSP or the length of an LC corresponds to the communicational complexity of an LSSS, one main motivation to study MSPs or LCs is the lower bound for their sizes or lengths. Therefore, it is one of the most important open problems how to efficiently construct an MSP or LC for a given access structure Γ with the smallest sizes or shortest length. Our contributions are: We extend TANG et al.’s result, showing that, for any given access structureΓ, there exists an MSP or an LC to realize Γ if and only if a system of quadratic equations has solutions; We utilize the relationship between LCs and MSPs to obtain the greatest lower bound on the row size and the column size of MSPs realizing a given Γ, as well as an upper bound on the column size of MSPs; We give an algorithm to construct an MSP with the smallest sizes.
It is shown that group covariant signals with respect to a specific group with the operation "Exclusive OR", which include binary linear codes as examples, satisfy the condition of the theorem 1 in [Phys. Re...
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It is shown that group covariant signals with respect to a specific group with the operation "Exclusive OR", which include binary linear codes as examples, satisfy the condition of the theorem 1 in [Phys. Rev. A 58 (1998) 146] and the minimum error detection is so-called square-root measurement. (C) 1999 Elsevier Science B.V. All rights reserved.
An algorithm for computing the weight distribution of a linear [n, k] code over a finite field F-q is developed. The codes are represented by their characteristic vector with respect to a given generator matrix and a ...
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An algorithm for computing the weight distribution of a linear [n, k] code over a finite field F-q is developed. The codes are represented by their characteristic vector with respect to a given generator matrix and a generator matrix of the k-dimensional simplex code S-q,S-k.
The nonexistence of a binary linear (15,6) code with covering radius 3 is proved by geometrically based arguments. The author also considers the wider application of the techniques.
The nonexistence of a binary linear (15,6) code with covering radius 3 is proved by geometrically based arguments. The author also considers the wider application of the techniques.<\n>
This correspondence deals with the fault-tolerant realization of a sequential machine using error-correcting (n,k) linear codes. Earlier works in the same area confine their attention to modified Reed-Muller code and ...
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This correspondence deals with the fault-tolerant realization of a sequential machine using error-correcting (n,k) linear codes. Earlier works in the same area confine their attention to modified Reed-Muller code and perfect Hamming code and achieve the realization using a number of majority logic gates, which makes the entire realization quite complex. The realization discussed in this paper needs a smaller number of circuit components with less complexity.
Systems glycobiology aims to provide models and analysis tools that account for the biosynthesis, regulation, and interactions with glycoconjugates. To facilitate these methods, there is a need for a clear glycan repr...
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Systems glycobiology aims to provide models and analysis tools that account for the biosynthesis, regulation, and interactions with glycoconjugates. To facilitate these methods, there is a need for a clear glycan representation accessible to both computers and humans. linear code, a linearized and readily parsable glycan structure representation, is such a language. For this reason, linear code was adapted to represent reaction rules, but the syntax has drifted from its original description to accommodate new and originally unforeseen challenges. Here, we delineate the consensuses and inconsistencies that have arisen through this adaptation. We recommend options for a consensus-based extension of linear code that can be used for reaction rule specification going forward. Through this extension and specification of linear code to reaction rules, we aim to minimize inconsistent symbology thereby making glycan database queries easier. With a clear guide for generating reaction rule descriptions, glycan synthesis models will be more interoperable and reproducible thereby moving glycoinformatics closer to compliance with FAIR standards. Here, we present linear code for Reaction Rules (LiCoRR), version 1.0, an unambiguous representation for describing glycosylation reactions in both literature and code.
Secret sharing has been a subject of study for over twenty years, and has a number of real-world applications. In this paper, a new class of linear code suitable for secret sharing scheme is presented, and the access ...
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ISBN:
(纸本)9781424447053
Secret sharing has been a subject of study for over twenty years, and has a number of real-world applications. In this paper, a new class of linear code suitable for secret sharing scheme is presented, and the access structure of the secret sharing scheme based on its dual is completely determined.
An invariant subcode of a linear block code under the permutation is introduced. The concept of invariant subcode has two types of applications. The first type is decoding of linear block codes given the group of symm...
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ISBN:
(数字)9783319393452
ISBN:
(纸本)9783319393452;9783319393445
An invariant subcode of a linear block code under the permutation is introduced. The concept of invariant subcode has two types of applications. The first type is decoding of linear block codes given the group of symmetry. The second type is the attack the McEliece cryptosystem based on codes correcting errors. Several examples illustrating the concept are presented.
In cryptographic field, it is open problem whether there is a linear code for given access structure Gamma, and how to construct if it exists. In this paper, we we mainly consider whether there is a linear code for gi...
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ISBN:
(纸本)9780769539829
In cryptographic field, it is open problem whether there is a linear code for given access structure Gamma, and how to construct if it exists. In this paper, we we mainly consider whether there is a linear code for given access structure Gamma. Our contributions are that we give two necessary and sufficient conditions for given access structure Gamma which exists a linear code in finite field F-2 and F-q(q not equal 2), respectively.
This paper deals with the construction of a class of binary uniquely decodable code pairs (C/sub 1/, C/sub 2/) for the two-user binary adder channel (2-BAC), where C/sub 1/ is a linear code. The generator matrix G for...
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This paper deals with the construction of a class of binary uniquely decodable code pairs (C/sub 1/, C/sub 2/) for the two-user binary adder channel (2-BAC), where C/sub 1/ is a linear code. The generator matrix G for code C/sub 1/ has the property that any of its columns has at most a single 1 among its K elements. These codes are called strongly orthogonal codes in the sense that the Hadamard product of any two rows of G is the all-zero n-tuple. The proposed 2-BAC codes achieve the upper bound for the sum rate when the rate of C/sub 1/ is greater than or equal to 1/2. Block and bit synchronization is assumed between the users and the receiver.
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