MinT - Information on Result #1117319

Information on Result #1117319

Linear OOA(3²³⁷, 5592440, F₃, 5, 12) (dual of [(5592440, 5), 27961963, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶⁵, 2796221, F₃, 5, 6) (dual of [(2796221, 5), 13981040, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵, 20, F₃, 5, 3) (dual of [(20, 5), 95, 4]-NRT-code), using
    - appending 2 arbitrary columns [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(3⁶⁰, 2796201, F₃, 5, 6) (dual of [(2796201, 5), 13980945, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(3⁶⁰, large, F₃, 6) (dual of [large, large−60, 7]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
linear OOA(3¹⁷², 2796220, F₃, 5, 12) (dual of [(2796220, 5), 13980928, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹⁰, 19, F₃, 5, 6) (dual of [(19, 5), 85, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 10, 19)-net over F₃, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(3¹⁶², 2796201, F₃, 5, 12) (dual of [(2796201, 5), 13980843, 13]-NRT-code), using
    - OOA 2-folding [i] based on 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.