Study On The Application Of Constacyclic Codes Over Finite Chain Rings Of Symbol-pair Distance And Secret Key Sharing

Recently,Cassuto and Blaum have proposed a symbol-pair model read channel,w-hich designed symbol-pair codes to prevent the symbol against error in the read cha-nnel.One of the most important tasks in the symbol-pair coding theory is to determine-the minimum symbol-pair distance of the symbol-pair code.The symbol-pair distan-ce is similar to the hamming distance.Therefore,it provides an important parameter to the error correction capability of the symbol-pair codes.In this paper,we mainly-study the symbol pairs distance of the cyclic codes and the constant cyclic codes ov-er theF2 + uF2,and accurately calculate the minimum symbol-pair distance of every k-ind of cyclic codes and constant cyclic codes.In the field of cryptography,a secret sharing scheme(k,n)is an agreement betwe-en a dealer and n participants,However,when the dealer fraud occurs,the false share-is allocated to the secret participant,and the secret will be damaged.Therefore,these secret sharing schemes require a reliable dealer to ensure the accu-racy of the secret share assigned to each participant.In this paper,second secret shar-ing schemes based on linear codes constructed by document[12]are added to the che-ckup algorithm,and the security analysis of the verified scheme is put forward,so as-to enhance the accuracy of the secret recovery.In addition,a new threshold secret s-haring scheme(l,t+/is proposed for the decoding algorithm based on error correcting codes in document[13].Based on this scheme Hash function is added to verify the c-orrectness and security of the scheme.