Abstract
Using geometric properties of the variety \({\mathcal V_{r,t}}\) , the image under the Grassmannian map of a Desarguesian (t − 1)-spread of PG(rt − 1, q), we introduce error correcting codes related to the twisted tensor product construction, producing several families of constacyclic codes. We determine the precise parameters of these codes and characterise the words of minimum weight.
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Communicated by G. Lunardon.
L. Giuzzi—Part of this research has been performed while a guest of the Department of Mathematics of Ghent University.
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Giuzzi, L., Pepe, V. Families of twisted tensor product codes. Des. Codes Cryptogr. 67, 375–384 (2013). https://doi.org/10.1007/s10623-012-9613-6
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DOI: https://doi.org/10.1007/s10623-012-9613-6
Keywords
- Segre product
- Veronesean
- Grassmannian
- Desarguesian spread
- Subgeometry
- Twisted product
- Constacyclic error correcting code
- Minimum weight