Direct products in projective Segre codes
نویسندگان
چکیده
منابع مشابه
Direct products in projective Segre codes
Let K = Fq be a finite field. We introduce a family of projective Reed-Muller-type codes called projective Segre codes. Using commutative algebra and linear algebra methods, we study their basic parameters and show that they are direct products of projective Reed-Mullertype codes. As a consequence we recover some results on projective Reed-Muller-type codes over the Segre variety and over proje...
متن کاملProjective Segre codes
Let K = Fq be a finite field. We introduce a family of projective Reed-Mullertype codes called projective Segre codes. Then we study their basic parameters and show that they are direct products of projective Reed-Muller-type codes. It turns out that the direct product of two projective Reed-Muller-type codes is again a projective Reed-Muller-type code. As a consequence we recover some results ...
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The recent interest both in partitions of finite geometries into other geometric objects and in the classical Segre varieties over finite fields are the background motivation for this paper. More precisely, partitions of Segre varieties into Segre varieties are investigated and the idea of nested partitions is introduced. Other partitions, namely of projective spaces and hyperbolic quadrics, ar...
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Let G = × i=1 Cli be the direct product of cycles. It is proved that for any r ≥ 1, and any n ≥ 2, each connected component of G contains an r-perfect code provided that each li is a multiple of r n +(r+1). On the other hand, if a code of G contains a given vertex and its canonical local vertices, then any li is a multiple of r + (r + 1). It is also proved that an r-perfect code (r ≥ 2) of G is...
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Invariant notions of a class of Segre varieties S(m)(2) of PG(2m − 1, 2) that are direct products of m copies of PG(1, 2), m being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains S(m)(2) and is invariant under its projective stabiliser group GS(m)(2). By embedding PG(2 m − 1, 2) into PG(2m − 1, 4), a basis of the latte...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2016
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2016.01.006