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
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.
