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Codes of bounded words (b-codes, ♦-codes), an extension of the notion of ordinary codes, have been first introduced and considered by P. T. Huy et al. in 2009. In this note, we consider some new subclasses of b-codes. In particular, characteristic properties of such codes are established. Also, relationships between b-codes, alternative codes and their subclasses are considered. | Journal of Computer Science and Cybernetics, V.33, N.3 (2017), 263–271 DOI 10.15625/1813-9663/33/3/10919 B-CODES AND THEIR RELATIONSHIP WITH ALTERNATIVE CODES NGO THI HIEN Ha Noi University of Science and Technology; hien.ngothi@hust.edu.vn Abstract. Codes of bounded words (b-codes, ♦-codes), an extension of the notion of ordinary codes, have been first introduced and considered by P. T. Huy et al. in 2009. In this note, we consider some new subclasses of b-codes. In particular, characteristic properties of such codes are established. Also, relationships between b-codes, alternative codes and their subclasses are considered. Keywords. Alternative code, b-code, norm b-code, two-side b-code, left b-code, strict b-code. Mathematics Subject Classification (2010): 94A45, 68Q45. 1. INTRODUCTION The theory of length-variable codes has been initiated by M. P. Sch¨ utzenberger in the 1950s and then developed by many others. A direction in this theory concentrates studying codes defined by control parameters or related with multi-value [1, 2, 4, 10, 13, 14, 16]. A code is a language such that every text encoded by words of the language can be decoded in a unique way. Codes are useful in many areas of application such as information processing, data compression, cryptography, information transmission and so on. For background of the theory of codes we refer to [3, 11, 15]. As mentioned above, the definition of codes is essentially based on unambiguity of the (catenation) product of words. Different modifications of such a product may lead to different extensions of the notion of codes. Such an approach has been proposed by P. T. Huy et al. which deals with the so-called even alternative codes and codes of bounded words (or ♦-codes, for short) [5, 6, 7, 10, 17, 18, 19, 20]. They demonstrated the importance characterizations as well as algorithms to test for these classes. For simplicity, ♦-codes, weak left ♦-codes, weak right ♦-codes and strict ♦-codes in [17, 18] are
