2010
DOI: 10.1016/j.jsc.2010.03.007
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The weight distributions of cyclic codes with two zeros and zeta functions

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Cited by 39 publications
(48 citation statements)
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“…There are a lot of references on the codes C (u,v,q,m) (see for example [2,20,28,29,[47][48][49][54][55][56]59,60]). It is obvious that C (u,v,q,m) cannot be a constant-weight code as its parity-check polynomial has two zeros.…”
Section: Three-weight Cyclic Codes Whose Duals Have Two Zerosmentioning
confidence: 99%
“…There are a lot of references on the codes C (u,v,q,m) (see for example [2,20,28,29,[47][48][49][54][55][56]59,60]). It is obvious that C (u,v,q,m) cannot be a constant-weight code as its parity-check polynomial has two zeros.…”
Section: Three-weight Cyclic Codes Whose Duals Have Two Zerosmentioning
confidence: 99%
“…In general, we have m 1 = m 2 = m. Thus the corresponding cyclic code C is an [n, 2m] code. If F called the dual of primitive cyclic code with two zeros had been studied in [9,13,14,18,62,63,74]. In this subsection, we only consider cyclic codes whose weight distributions are determined by Gauss periods, so we do not describe the results on primitive cyclic codes here.…”
Section: Gauss Periods and Weight Distributionsmentioning
confidence: 99%
“…For the weight distributions of the cyclic codes with two nonzeros α −(2 2·1 +1) and α −(2 1 +1) , there are the following results in [2]. For m = 7, the corresponding cyclic code C 1 has three nonzero weights and Using Matlab, it can be found that the cyclic code with nonzeros α −(2 2·3 +1) and α −(2 3 +1) has the same weight distribution as C 1 for m = 7, and C 2 for m = 11.…”
Section: Resultsmentioning
confidence: 99%
“…In this note we study the case k = 3. Boston and McGuire considered the weight distributions of binary cyclic codes with at most five nonzero weights [2]. For relevant studies of cyclic codes, please refer to [3]- [5], [14], [15], [18]- [20].…”
Section: Conjecturementioning
confidence: 99%