MinT - Information on Result #1119472

Information on Result #1119472

Linear OOA(3¹²⁶, 4194548, F₃, 5, 9) (dual of [(4194548, 5), 20972614, 10]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁸, 248, F₃, 5, 3) (dual of [(248, 5), 1232, 4]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(3⁸, 248, F₃, 3, 3) (dual of [(248, 3), 736, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(3⁸, 248, F₃, 2, 3) (dual of [(248, 2), 488, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁸, 248, F₃, 3) (dual of [248, 240, 4]-code or 248-cap in PG(7,3)), using
      - large caps in PG(u,Â 3) [i]
linear OOA(3²⁸, 2097150, F₃, 5, 4) (dual of [(2097150, 5), 10485722, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²⁸, 2391484, F₃, 5, 4) (dual of [(2391484, 5), 11957392, 5]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(3²⁸, 2391485, F₃, 2, 4) (dual of [(2391485, 2), 4782942, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (24, 28, 2391485)-net over F₃, using
      - nets constructed from net-embeddable BCH codes [i]
linear OOA(3⁹⁰, 2097150, F₃, 5, 9) (dual of [(2097150, 5), 10485660, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3⁹⁰, 8388601, F₃, 9) (dual of [8388601, 8388511, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁹⁰, large, F₃, 9) (dual of [large, large−90, 10]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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.