MinT - Information on Result #1010789

Information on Result #1010789

Linear OOA(3²²⁶, 5592424, F₃, 3, 15) (dual of [(5592424, 3), 16777046, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶⁶, 2796221, F₃, 3, 7) (dual of [(2796221, 3), 8388597, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. 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(3⁶¹, 2796201, F₃, 3, 7) (dual of [(2796201, 3), 8388542, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(3⁶¹, large, F₃, 7) (dual of [large, large−61, 8]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
linear OOA(3¹⁶⁰, 2796212, F₃, 3, 15) (dual of [(2796212, 3), 8388476, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹⁰, 11, F₃, 3, 7) (dual of [(11, 3), 23, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (3, 10, 11)-net over F₃, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(3¹⁵⁰, 2796201, F₃, 3, 15) (dual of [(2796201, 3), 8388453, 16]-NRT-code), using
    - OOA 3-folding [i] 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.