No abstract

Line codes are widely used to protect against errors in data transmission and storage systems, to ensure the stability of various cryptographic algorithms and protocols, to protect hidden information from errors in a stegocontainer. One of the classes of codes that nd application in a number of the listed areas is the class of linear self-complementary codes over a binary eld. Such codes contain a vector of all ones, and their weight enumerator is a symmetric polynomial. In applied problems, self-complementary [ , ]-codes are o en required for a given length n and dimension k to have the maximum possible code distance ( , ). For < 13, the values of ( , ) are already known. In this paper, for self-complementary codes of length n=13, 14, 15, the problem is to nd lower bounds on ( , ), as well as to nd the values of ( , ) themselves.e development of an e cient method for obtaining a lower estimate close to ( , ) is an urgent task, since nding the values of ( , ) in the general case is a di cult task. e paper proposes four methods for nding lower bounds: based on cyclic codes, based on residual codes, based on the (u-u+v)-construction, and based on the tensor product of codes. On the joint use of these methods for the considered lengths, it was possible to e ciently obtain lower bounds, either coinciding with the found values of ( , ) or di ering by one. e paper proposes a sequence of checks, which in some cases helps to prove the absence of a self-complementary [ , ]-code with code distance d. In the nal part of the work, on the basis of self-complementary codes, a design for hiding information is proposed that is resistant to interference in the stegocontainer.e above calculations show the greater e ciency of the new design compared to the known designs.

We consider a model of protecting the confidentiality and recoverability of data in a distributed storage system. It is assumed that informational blocks are coded into the code blocks. Then the blocks are divided into parts and distributed among repositories of the distributed storage. A modification of the code noising method is constructed which simultaneously provides computational resistance to coalition attacks on confidentiality of stored data. Moreover, the modification also provides protection from the failure of a part of the storage nodes. Confidentiality protection is provided for coalitions of greater cardinality than in the case of using the classical method of code noising. It is shown that computational resistance is based on the complexity of solving one well-known problem of theoretical coding.