Abstract
A method is given for the construction of linear codes with prescribed minimum distance and also prescribed minimum distance of the dual code. This works for codes over arbitrary finite fields. In the case of binary codes Matsumoto et al. showed how such codes can be used to construct cryptographic Boolean functions. This new method allows to compute new bounds on the size of such codes, extending the table of Matsumoto et al..
Funding Statement
The author wants to thank the NATO for providing a grant to cover travel costs.
Acknowledgment
The author thanks Ryutaroh Matsumoto for his helpful comments and for providing a copy of his program for the calculation of the linear programming bound from [16] which we used in section 5.
Citation
Axel Kohnert. "CONSTRUCTION OF LINEAR CODES HAVING PRESCRIBED PRIMAL-DUAL MINIMUM DISTANCE WITH APPLICATIONS IN CRYPTOGRAPHY." Albanian J. Math. 2 (3) 221 - 227, 2008. https://doi.org/10.51286/albjm/1229509503
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