Direct products in projective Segre codes (Q268479)
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scientific article; zbMATH DE number 6569342
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Direct products in projective Segre codes |
scientific article; zbMATH DE number 6569342 |
Statements
Direct products in projective Segre codes (English)
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15 April 2016
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Reed-Muller code
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Segre code
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direct product
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Segre embedding
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finite field
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minimum distance
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Hilbert function
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tensor product
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The authors consider a new family of codes, projective Segre codes, the Segre embedding of two projective Reed-Muller codes. The authors show that a Segre code is equal to the Segre product of the two Reed-Muller codes that defined the Segre code (direct products of projective Reed-Muller type codes).NEWLINENEWLINEThe parameters of a Segre code (length, dimension, minimum distance) are given in terms of the two projective Reed-Muller codes used to define the Segre code. The mathematical tools are Hilbert functions, resolutions and Gröbner bases.
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