MinT - Information on Result #1189780

Information on Result #1189780

Digital (27, 34, 5651)-net over F₇, using net defined by OOA based on linear OOA(7³⁴, 5651, F₇, 9, 7) (dual of [(5651, 9), 50825, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(7³⁴, 5652, F₇, 3, 7) (dual of [(5652, 3), 16922, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7⁴, 50, F₇, 3, 3) (dual of [(50, 3), 146, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(7⁴, 50, F₇, 2, 3) (dual of [(50, 2), 96, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(7⁴, 50, F₇, 3) (dual of [50, 46, 4]-code or 50-cap in PG(3,7)), using
        ovoid in PG(3,Â 7) [i]
  2. linear OOA(7³⁰, 5602, F₇, 3, 7) (dual of [(5602, 3), 16776, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(7³⁰, 16806, F₇, 7) (dual of [16806, 16776, 8]-code), using
      - 1 times truncation [i] based on linear OA(7³¹, 16807, F₇, 8) (dual of [16807, 16776, 9]-code), using
        an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.