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...
详细信息
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.
A secret sharing system can be damaged when the dealer cheating *** this paper,two kinds of secret sharing schemes based on linear code are *** is a verifiable scheme which each participant can verify his own share fr...
详细信息
A secret sharing system can be damaged when the dealer cheating *** this paper,two kinds of secret sharing schemes based on linear code are *** is a verifiable scheme which each participant can verify his own share from dealer's distribution and ensure each participant to receive valid *** does not have a trusted center,here,each participant plays a dual-role as the dealer and shadow(or share) provider in the whole scheme.
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 ...
详细信息
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.
In this paper we consider an error-detecting code based on linear quasigroups. Namely, each input block a0a1 horizontal ellipsis an-1 is extended into a block a0a1 horizontal ellipsis an-1d0d1 horizontal ellipsis dn-1...
详细信息
In this paper we consider an error-detecting code based on linear quasigroups. Namely, each input block a0a1 horizontal ellipsis an-1 is extended into a block a0a1 horizontal ellipsis an-1d0d1 horizontal ellipsis dn-1, where the redundant characters d0,d1, horizontal ellipsis ,dn-1 are defined with di=ai*ai+1*ai+2, where * is a linear quasigroup operation and the operations in the indexes are modulo n. We give a proof that under some conditions the code is linear. Using this fact, we contribute to the determination of the error-detecting capability of the code. Namely, we determine the Hamming distance of the code and from there we obtain the number of errors that the code will detect for sure when linear quasigroups of order 4 from the best class of quasigroups of order 4 for which the constant term in the linear representation is zero matrix are used for coding. All results in the paper are derived for arbitrary length of the input blocks. With the obtained results we showed that when a small linear quasigroup of order 4 from the best class of quasigroups of order 4 is used for coding, the number of errors that the code surely detects is upper bounded with 4.
In this paper for an arbitrary linear separable code the concept of a code Preserving Multi-Input Signature Register COPMISR is introduced. For a code with k control bits 2/sup k2/ different COPMISR's can be desig...
详细信息
In this paper for an arbitrary linear separable code the concept of a code Preserving Multi-Input Signature Register COPMISR is introduced. For a code with k control bits 2/sup k2/ different COPMISR's can be designed. The optimum COPMISR with a minimum number of XOR-gates can be chosen from this large set. By different examples it is shown how the newly introduced COPMISR can be simultaneously utilized for concurrent checking, testing and localization of an eventually erroneous component of the monitored system. Since parity codes, group-parity codes, duplication codes and Hamming codes are special linear separable codes the concept of the COPMISR has a wide range of applications in different areas of on-line error detection and BIST.
Let E/sub m/ denote the binary (m, m-1, 2) even weight code and /spl ominus/ the Kronecker product operation. A linear code of length m/spl times/t containing E/sub m//spl ominus/(t,1,t) can be decoded efficiently usi...
详细信息
Let E/sub m/ denote the binary (m, m-1, 2) even weight code and /spl ominus/ the Kronecker product operation. A linear code of length m/spl times/t containing E/sub m//spl ominus/(t,1,t) can be decoded efficiently using a Tanner graph and a trellis diagram together with the Wagner decoding algorithm. Thus, it is important to determine whether a given code contains such a subcode. We show that the (18,9,6) binary quadratic residue code does not contain E/sub 6//spl ominus/(3,1,3). The maximum minimum distance of such a code is 5.
An algorithm for finding minimum-weight words in large linear codes is developed. It is pointed out that the original McEliece (1978) cryptosystem is not secure. We also determine the minimum distance of some BCH code...
详细信息
An algorithm for finding minimum-weight words in large linear codes is developed. It is pointed out that the original McEliece (1978) cryptosystem is not secure. We also determine the minimum distance of some BCH codes of length 511.
In cryptographic field, it is open problem whether there is a linear code for given access structure ¿, and how to construct if it exists. In this paper, we mainly consider whether there is a linear code for give...
详细信息
ISBN:
(纸本)9781424460793
In cryptographic field, it is open problem whether there is a linear code for given access structure ¿, and how to construct if it exists. In this paper, we mainly consider whether there is a linear code for given access structure ¿. Our contributions are that we give two necessary and sufficient conditions for given access structure ¿ which exists a linear code in finite field F 2 and F q (q ¿ 2), respectively.
An efficient algorithm for calculating the i-th bit error probability of a binary linear code over the binary symmetric channel (BSC) are presented. It is proved that the exact i-th bit error probability of maximum li...
详细信息
An efficient algorithm for calculating the i-th bit error probability of a binary linear code over the binary symmetric channel (BSC) are presented. It is proved that the exact i-th bit error probability of maximum likelihood (ML) decoding, bounded distance decoding, symbolwise maximum a posteriori probability (MAP) decoding and symbolwise MAP decoding with erasure can be obtained with time complexity O(n2/sup n-k/), where n, k denote length and dimension of the target code.
In this paper, the update complexity of a linear code ensemble (binary or nonbinary) is considered. The update complexity has been proposed in [1] as a measure of the number of updates needed to be done within the bit...
详细信息
In this paper, the update complexity of a linear code ensemble (binary or nonbinary) is considered. The update complexity has been proposed in [1] as a measure of the number of updates needed to be done within the bits of a codeword, if one of information bits, encoded in this codeword, has been changed. The update efficiency is a performance measure of distributed storage applications, that naturally use erasure-correction coding. The maximum update complexity γmax and the average update complexity γavg of a code ensemble are distinguished in this paper. In the first part of the paper, we propose a simple lower bound on the γavg and further evaluate its general expression. In the second part, we show how a simple upper bound on γavg for sparse graph codes can be obtained, on a particular example of binary LDPC codes. One of interesting results of the paper is that code ensembles with polynomial minimum distance growth have the update complexity which grows linearly in the codelength, i.e. they are not update-efficient.
暂无评论