Vladimir D. Tonchev

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This paper studies self-dual and maximal self-orthogonal codes over GF(3). First, a number of Gleason-type theorems are given, describing the weight enumerators of such codes. Second, a table of all such codes of length _-<12 is constructed. Finally, the complete weight enumerators of various quadratic residue and symmetry codes of length =<60.are obtained.
The terminology and notations from design theory used in this paper are in accordance with those in Beth, Jungnickei, and Lenz [3], Cameron and van Lint [4], Hughes and Piper [6]. One of the most important examples of Steiner systems is the celebrated S(5, 8, 24) constructed by Witt in 1938 using the Mathieu group M,,. Applying consecutive derivation to an(More)
Difference Systems of Sets (DSS) are combinatorial configurations that arise in connection with code synchronization. This paper gives new constructions of DSS obtained from partitions of hyperplanes in a finite projective space, as well as DSS obtained from balanced generalized weighing matrices and partitions of the complement of a hyperplane in a finite(More)
Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously known general framework for designing quantum synchronizable codes through more extensive use of the theory of finite fields. This makes it possible to widen the range of tolerable(More)
where (a,O) E A P l ) , ( O , b ) E Bil) , (c , l ) E A P 1 ) , ( l , d ) E Obviously, the code has IAP’)l P6’’1 + /AY1)] (B[’)I codewords. Cohen et al. [5 ] proved that the code has covering radius less or equal R1 + R2. If the covering radius of the new code is RI + R2, then the new code is also normal. Usually, the codes obtained from P(n) , D(n ) , E ((More)