The weight distribution of a family of $$p$$ p -ary cyclic codes

The weight enumerators of several classes of p-ary cyclic codes

“…Basically, the weight distribution is connected to the value distribution of certain exponential sum, which is generally hard to be determined explicitly. For the duals of primitive cyclic codes with few quadratic type zeros, their weight distributions have been intensively studied, for example see [1,4,13,7,12,23,26,25,27,28] and references therein. For the duals of primitive cyclic codes with few non-quadratic type zeros, the reader is referred to [3,6,10,16,18,22,24] and references therein.…”

Constant composition codes as subcodes of linear codes

“…So, the corrosponing exponential sums can be computed by some technologies of finite field. Therefore, the weight distributions of a large number of linear codes (cyclic codes) were obtained (see [5,6,8,9,11,12,14,15,[17][18][19][20][21][22], and references theirin).…”

The weight distributions of two classes of binary cyclic codes

“…For reducible cyclic codes with few nonzeros over finite fields of odd characteristic, their weight distributions have been intensively studied recently, for example see [2,5,[12][13][14][15][16]19,20,22,[27][28][29][30][31][32] and references therein. For reducible cyclic codes with few nonzeros over finite fields of even characteristic, there are also some important results, including [6][7][8][9]11,17,23,25] and references therein.…”