BUILDING A QUALITY ASSESSMENT CRITERION BINARY BARKER-LIKE CODES

Abstract

The objective of this article is to construct a criterion for evaluating the quality of binary Barker-like codes. The analysis of well-known studies on the formation of these codes with properties close to binary Barker codes is carried out. The analysis showed that in the works devoted to the use of well-known binary Barker-like codes in secure wireless communication systems and the formation of such codes, researchers primarily pay attention to such quality assessment indicators as the autocorrelation function, the length and number of such codes, and others. Based on the analysis of works [5, 9-25], the initial tuple of quality assessment of binary Barker-like codes is formulated, represented by the expression (1). However, the original tuple (1) lacks such an important quality assessment indicator as the linear complexity assessment, which is often taken as one of the primary indicators of crypto resistance. Based on this, the purpose of this article is to increase the accuracy of the evaluation of binary Barker-like codes by applying the identified criterion. The authors of the article, using the Berlekamp-Massey algorithm, evaluated the linear complexity of binary Barker-like codes presented in [9-23]. It has been established that a sufficiently large number of such codes (from 24% to 75%) have insufficient linear complexity, that is, they are non-cryptographic. As a result, they cannot be used in secure wireless communication systems. The result obtained is consistent with other studies in this field. Proceeding from this, when using well-known binary Barker-like codes in secure wireless communication systems, as well as when forming new binary Barker-like codes, it is necessary to pay attention not only to the known quality assessment indicators, but also to their linear complexity. The authors have modified the original tuple represented by expression (1). The modified tuple is represented by expression (2). According to the authors, the modified quality assessment criterion will improve the accuracy of the evaluation of binary Barker-like codes.