MinT - Information on Result #1081062

Information on Result #1081062

Linear OOA(3¹⁷⁹, 4194354, F₃, 4, 12) (dual of [(4194354, 4), 16777237, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁷, 53, F₃, 4, 6) (dual of [(53, 4), 195, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵, 20, F₃, 4, 3) (dual of [(20, 4), 75, 4]-NRT-code), using
    - appending 1 arbitrary column [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(3¹², 33, F₃, 4, 6) (dual of [(33, 4), 120, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 12, 33)-net over F₃, using
      - linear code embedding found in a computer search [i]
linear OOA(3¹⁶², 4194301, F₃, 4, 12) (dual of [(4194301, 4), 16777042, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3¹⁶², 8388602, F₃, 2, 12) (dual of [(8388602, 2), 16777042, 13]-NRT-code), using
  - trace code [i] based on linear OOA(9⁸¹, 4194301, F₉, 2, 12) (dual of [(4194301, 2), 8388521, 13]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(9⁸¹, 8388602, F₉, 12) (dual of [8388602, 8388521, 13]-code), using
      - discarding factors / shortening the dual code based on linear OA(9⁸¹, large, F₉, 12) (dual of [large, large−81, 13]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 9⁸âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.