In this paper using the weight enumerators of a linear [n, k]--code, we give a theorem about minimal codewords. In this n context, we show that while 1 E C if Wmin〉 n/2 in the binary [n, k] --code C, then all of the...In this paper using the weight enumerators of a linear [n, k]--code, we give a theorem about minimal codewords. In this n context, we show that while 1 E C if Wmin〉 n/2 in the binary [n, k] --code C, then all of the nonzero codewords of C are 2 minimal. Therefore, we obtain a corollary.展开更多
In this paper, we show that if Wmax 〈 6 for the Hamming code Ham （r, 2）, then all of the nonzero codewords of Ham （r, 2） are minimal and if Wrnax 〈 8 for the extended Hamming code Hfim （r, 2）, then all of the ...In this paper, we show that if Wmax 〈 6 for the Hamming code Ham （r, 2）, then all of the nonzero codewords of Ham （r, 2） are minimal and if Wrnax 〈 8 for the extended Hamming code Hfim （r, 2）, then all of the nonzero codewords ofHfim （r, 2） are minimal, where Wmax is the maximum nonzero weight in Ham （r, 2） and Hfim （r, 2）.展开更多
文摘In this paper using the weight enumerators of a linear [n, k]--code, we give a theorem about minimal codewords. In this n context, we show that while 1 E C if Wmin〉 n/2 in the binary [n, k] --code C, then all of the nonzero codewords of C are 2 minimal. Therefore, we obtain a corollary.
文摘In this paper, we show that if Wmax 〈 6 for the Hamming code Ham （r, 2）, then all of the nonzero codewords of Ham （r, 2） are minimal and if Wrnax 〈 8 for the extended Hamming code Hfim （r, 2）, then all of the nonzero codewords ofHfim （r, 2） are minimal, where Wmax is the maximum nonzero weight in Ham （r, 2） and Hfim （r, 2）.
