MinT - Information on Result #1117590

Information on Result #1117590

Linear OOA(3¹⁶⁸, 1677766, F₃, 5, 15) (dual of [(1677766, 5), 8388662, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁸, 46, F₃, 5, 7) (dual of [(46, 5), 212, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵, 20, F₃, 5, 3) (dual of [(20, 5), 95, 4]-NRT-code), using
    - appending 2 arbitrary columns [i] based on linear OOA(3⁵, 20, F₃, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(3⁵, 20, F₃, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] 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]
  2. linear OOA(3¹³, 26, F₃, 5, 7) (dual of [(26, 5), 117, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 13, 26)-net over F₃, using
      - linear code embedding found in a computer search [i]
linear OOA(3¹⁵⁰, 1677720, F₃, 5, 15) (dual of [(1677720, 5), 8388450, 16]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁵⁰, 8388600, F₃, 15) (dual of [8388600, 8388450, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁵⁰, large, F₃, 15) (dual of [large, large−150, 16]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.

Other Results with Identical Parameters

None.

Depending Results

None.