MinT - Information on Result #661850

Information on Result #661850

Linear OA(3³⁴, 93, F₃, 11) (dual of [93, 59, 12]-code), using (u,Â uâˆ’v,Â u+v+w)-construction based on

linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
- doubling the cap [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
  - ovoid in PG(3,Â 3) [i]
linear OA(3⁸, 28, F₃, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by constructionÂ Y1) [i] based on
  1. linear OA(3²⁰, 28, F₃, 14) (dual of [28, 8, 15]-code), using
    - contraction [i] based on linear OA(3⁴⁸, 56, F₃, 29) (dual of [56, 8, 30]-code), using the BCH-code C(I) with length 56Â | 3⁶âˆ’1, defining interval IÂ =Â {0,1,…,28}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
  2. nonexistence of linear OA(3¹⁹, 23, F₃, 14) (dual of [23, 4, 15]-code), because
    - 2 times truncation [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
      - â€œHNâ€ bound on codes from Brouwerâ€™s database [i]
linear OA(3²¹, 45, F₃, 11) (dual of [45, 24, 12]-code), using
- 3 times truncation [i] based on linear OA(3²⁴, 48, F₃, 14) (dual of [48, 24, 15]-code), using
  - extended quadratic residue code Q_e(48,3) [i]

Mode: Constructive and linear.

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