On the Number of Two-Weight Cyclic Codes with Composite Parity-Check Polynomials
Sufficient conditions for the construction of a two-weight cyclic code by means of the direct sum of two one-weight cyclic codes, were recently presented in . On the other hand, an explicit formula for the number of one-weight cyclic codes, when the length and dimension are given, was proved in . By imposing some conditions on the finite field, we now combine both results in order to give a lower bound for the number of two-weight cyclic codes with composite parity-check polynomials.
KeywordsOne-weight cyclic codes two-weight cyclic codes
Unable to display preview. Download preview PDF.
- 4.Vega, G.: Two-weight cyclic codes constructed as the direct sum of two one-weight cyclic codes, Finite Fields Appl. (in press, 2008), doi:10.1016/j.ffa.2008.01.002Google Scholar