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   Enumeration of symmetric (45,12,3) designs with nontrivial automorphisms  
   
نویسنده crnkovic dean ,danilovic doris dumicic ,rukavina sanja
منبع journal of algebra combinatorics discrete structures and applications - 2016 - دوره : 3 - شماره : 3 - صفحه:145 -154
چکیده    We show that there are exactly 4285 symmetric (45,12,3) designs that admit nontrivial automorphisms. among them there are 1161 self-dual designs and 1562 pairs of mutually dual designs. we describe the full automorphism groups of these designs and analyze their ternary codes. r. mathon and e. spence have constructed 1136 symmetric (45,12,3) designs with trivial automorphism group, which means that there are at least 5421 symmetric (45,12,3) designs. further, we discuss trigeodetic graphs obtained from the symmetric (45; 12; 3) designs. we prove that k-geodetic graphs constructed from mutually non-isomorphic designs are mutually non-isomorphic, hence there are at least 5421 mutually non-isomorphic trigeodetic graphs obtained from symmetric (45; 12; 3) designs.
کلیدواژه Symmetric design ,Linear code ,Automorphism group ,k-geodetic graph
آدرس university of rijeka, department of mathematics, Croatia, university of rijeka, department of mathematics, Croatia, university of rijeka, department of mathematics, Croatia
 
     
   
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