MinT - Information on Result #1100853

Information on Result #1100853

Linear OOA(3¹⁷⁹, 2796227, F₃, 5, 12) (dual of [(2796227, 5), 13980956, 13]-NRT-code), using OOA 2-folding based on linear OOA(3¹⁷⁹, 5592454, F₃, 3, 12) (dual of [(5592454, 3), 16777183, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁷⁹, 5592455, F₃, 3, 12) (dual of [(5592455, 3), 16777186, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹⁷, 53, F₃, 3, 6) (dual of [(53, 3), 142, 7]-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(3¹², 33, F₃, 3, 6) (dual of [(33, 3), 87, 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]
  2. linear OOA(3¹⁶², 5592402, F₃, 3, 12) (dual of [(5592402, 3), 16777044, 13]-NRT-code), using
    - trace code [i] based on linear OOA(9⁸¹, 2796201, F₉, 3, 12) (dual of [(2796201, 3), 8388522, 13]-NRT-code), using
      - OOA 3-folding [i] 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.