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Spin-embeddings, two-intersection sets and two-weight codes

(2013) ARS COMBINATORIA. 109. p.309-319
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Abstract
Let Delta be one of the dual polar spaces DQ(8, q), DQ(-) (7, q), and let e : Delta -> Sigma denote the spin-embedding of Delta. We show that e(Delta) is a two-intersection set of the projective space Sigma. Moreover, if Delta congruent to DQ(-) (7, q), then e(Delta) is a (q(3) + 1)-tight set of a nonsingular hyperbolic quadric Q(+) (7, q(2)) of Sigma congruent to PG(7, q(2)). This (q(3) + 1)-tight set gives rise to more examples of (q(3) + 1)-tight sets of hyperbolic quadrics by a procedure called field-reduction. All the above examples of two-intersection sets and (q(3) + 1)-tight sets give rise to two-weight codes and strongly regular graphs.
Keywords
dual polar space, spin-embedding, two-intersection set, two-weight code, strongly regular graph, tight set, DUAL POLAR SPACES, HYPERPLANES

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Citation

Please use this url to cite or link to this publication:

Chicago
Cardinali, Ilaria, and Bart De Bruyn. 2013. “Spin-embeddings, Two-intersection Sets and Two-weight Codes.” Ars Combinatoria 109: 309–319.
APA
Cardinali, I., & De Bruyn, B. (2013). Spin-embeddings, two-intersection sets and two-weight codes. ARS COMBINATORIA, 109, 309–319.
Vancouver
1.
Cardinali I, De Bruyn B. Spin-embeddings, two-intersection sets and two-weight codes. ARS COMBINATORIA. 2013;109:309–19.
MLA
Cardinali, Ilaria, and Bart De Bruyn. “Spin-embeddings, Two-intersection Sets and Two-weight Codes.” ARS COMBINATORIA 109 (2013): 309–319. Print.
@article{4241842,
  abstract     = {Let Delta be one of the dual polar spaces DQ(8, q), DQ(-) (7, q), and let e : Delta -{\textrangle} Sigma denote the spin-embedding of Delta. We show that e(Delta) is a two-intersection set of the projective space Sigma. Moreover, if Delta congruent to DQ(-) (7, q), then e(Delta) is a (q(3) + 1)-tight set of a nonsingular hyperbolic quadric Q(+) (7, q(2)) of Sigma congruent to PG(7, q(2)). This (q(3) + 1)-tight set gives rise to more examples of (q(3) + 1)-tight sets of hyperbolic quadrics by a procedure called field-reduction. All the above examples of two-intersection sets and (q(3) + 1)-tight sets give rise to two-weight codes and strongly regular graphs.},
  author       = {Cardinali, Ilaria and De Bruyn, Bart},
  issn         = {0381-7032},
  journal      = {ARS COMBINATORIA},
  language     = {eng},
  pages        = {309--319},
  title        = {Spin-embeddings, two-intersection sets and two-weight codes},
  volume       = {109},
  year         = {2013},
}

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