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   Cyclotomic Cosets,Codes and Secret Sharing  
نویسنده Wong D.C.K.
منبع Malaysian Journal Of Mathematical Sciences - 2017 - دوره : 11 - شماره : S - صفحه:59 -73
چکیده    In this paper,all 2-cyclotomic cosets modulo pn are constructed when 2 is a primitive root modulo pn. when the order of 2 is p-1/2 modulo p and the order of 2 is p(p-1)/2 modulo p2,we construct all 2-cyclotomic cosets modulo p2. also,when 2 has order p2(p-1)/2 modulo p3,we derive all 2-cyclotomic cosets modulo p3. furthermore,four results on all s-cyclotomic cosets modulo pq are obtained by considering three different possible orders of s modulo p and q,for distinct odd primes p,q. finally,we use the 2-cyclotomic cosets modulo 9,25 and 49 to construct binary codes of length 9,15 and 49,respectively,and hence the access sets for the secret sharing scheme based on some of these families of binary codes are discussed.
کلیدواژه Cyclic Codes; Cyclotomic Cosets; Idem- Potents; Minimum Distance; Secret Sharing
آدرس Lee Kong Chian Faculty Of Engineering And Science,Universiti Tunku Abdul Rahman,Jalan Sungai Long,Cheras,Kajang,Selangor Darul Ehsan, Malaysia

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