In this paper,we calculate the number of the codewords(with Hamming weight 7)of each type in the Preparata codes over Z4,then give the parameter sets of 3-designs constructed from the supports of the codewords of each...In this paper,we calculate the number of the codewords(with Hamming weight 7)of each type in the Preparata codes over Z4,then give the parameter sets of 3-designs constructed from the supports of the codewords of each type.Moreover,we prove that the first two families of 3-designs are simple and the third family of the 3-designs has repeated blocks.展开更多
This paper constructs a cyclic Z_4-code with a parity-check matrix similar to that of Goethals code but in length 2~m+ 1, for all m ≥ 4. This code is a subcode of the lifted Zetterberg code for m even. Its minimum Le...This paper constructs a cyclic Z_4-code with a parity-check matrix similar to that of Goethals code but in length 2~m+ 1, for all m ≥ 4. This code is a subcode of the lifted Zetterberg code for m even. Its minimum Lee weight is shown to be at least 10, in general, and exactly 12 in lengths 33, 65. The authors give an algebraic decoding algorithm which corrects five errors in these lengths for m = 5, 6 and four errors for m > 6.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11071163)Doctor Fund of Shandong Province(Grant No.BS2009SF017)
文摘In this paper,we calculate the number of the codewords(with Hamming weight 7)of each type in the Preparata codes over Z4,then give the parameter sets of 3-designs constructed from the supports of the codewords of each type.Moreover,we prove that the first two families of 3-designs are simple and the third family of the 3-designs has repeated blocks.
文摘This paper constructs a cyclic Z_4-code with a parity-check matrix similar to that of Goethals code but in length 2~m+ 1, for all m ≥ 4. This code is a subcode of the lifted Zetterberg code for m even. Its minimum Lee weight is shown to be at least 10, in general, and exactly 12 in lengths 33, 65. The authors give an algebraic decoding algorithm which corrects five errors in these lengths for m = 5, 6 and four errors for m > 6.
