Bounds Of Wide-Sense 2-Separable Codes

With the development of communications and network technologies,the number of data information transmissions is also increasing,but in the process of information dissemination,illegal situations such as information theft and dissemination are also endlessly measured.When encrypting information using traditional encryption technology,the distributor transmits the encrypted information to the authorized user.Once the authorized user decrypts the encrypted information,the information can be unlimitedly authorized by the authorized user without the permission of the distributor.For illegal sharing,the rights and interests of distributors cannot be guaranteed.In response to this situation,many scholars have conducted research on it,resulting in the successful exploration of digital fingerprint technology.Digital fingerprint technology refers to that the distributor embeds a unique identifier into the information before transmitting the information to each authorized user,so as to mark the user.This technology can effectively prevent illegal users from maliciously disseminating data information and protect intellectual property rights.Therefore,an indispensable tool for this technology to achieve is the fingerprinting code.In fact,the fingerprinting code serves as the object mentioned above.In recent years,the research on fingerprinting codes is also very extensive,and has achieved good results.A fingerprinting code introduced in this paper is the separable code,which can be used to identify illegal users and effectively prevent the illegal dissemination of data information.The content in this paper is mainly developed by the separable code with the number of coalitions t under the wide-sense descendant model,especially the wide-sense 2-separable code(2-w S C).The specific content of this paper is divided as follows:The first chapter introduces the research background and significance of the selected topic,the research status of separable codes,the definition of separable codes under four descendant models and proves the relationship between these separable codes.At present,most of the researches on separable codes are focused on narrow-sense separable codes,and the research object of this paper is wide-sense separable codes.The second chapter mainly proves the relationship between separable codes and other fingerprinting codes,especially 2-resilient-LACC and frameproof codes.Furthermore,this expands the relationship between fingerprinting codes.The third chapter mainly focuses on the construction and lower bounds of 2-w S Cs.By introducing the coincidence function,the corresponding relation of 2-w S C in set theory is found.Furthermore,by studying the properties of the family of coincident functions on 2-w S C,the construction and lower bounds of 2-w S Cs are obtained.Chapter 4 is the study of the upper bounds of 2-w S Cs.Using the definition of 2-w S C combined with the difference set method,an upper bound on code capacity is obtained.At the same time,according to the method of coincidence function in Chapter 3,the upper bounds of 2-w S Cs is given.Chapter 5 elaborates the conclusions of this paper,especially the innovations in the text.And gives the research directions in the future.