Determining the Number of One-Weight Cyclic Codes When Length and Dimension Are Given
We use techniques from linear recurring sequences, exponential sums and Gaussian sums, in order to present a set of characterizations for the one-weight irreducible cyclic codes over finite fields. Without using such techniques, a subset of these characterizations was already presented in . By means of this new set of characterizations, we give an explicit expression for the number of one-weight cyclic codes, when the length and dimension are given.
KeywordsOne-weight cyclic codes linear recurring sequences exponential sums and Gaussian sums
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