MinT - Information on Result #1010784

Information on Result #1010784

Linear OOA(3²²³, 5592416, F₃, 3, 15) (dual of [(5592416, 3), 16777025, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶⁵, 2796211, F₃, 3, 7) (dual of [(2796211, 3), 8388568, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁴, 10, F₃, 3, 3) (dual of [(10, 3), 26, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(3⁴, 10, F₃, 2, 3) (dual of [(10, 2), 16, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [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(3¹⁵⁸, 2796208, F₃, 3, 15) (dual of [(2796208, 3), 8388466, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁸, 7, F₃, 3, 7) (dual of [(7, 3), 13, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,13P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
      - an explicitly constructive algebraic function field [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.