MinT - Information on Result #1016097

Information on Result #1016097

Linear OOA(9¹⁰⁶, 5592648, F₉, 3, 12) (dual of [(5592648, 3), 16777838, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9¹⁶, 246, F₉, 3, 6) (dual of [(246, 3), 722, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(9⁴, 82, F₉, 3, 3) (dual of [(82, 3), 242, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(9⁴, 82, F₉, 2, 3) (dual of [(82, 2), 160, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(9⁴, 82, F₉, 3) (dual of [82, 78, 4]-code or 82-cap in PG(3,9)), using
        ovoid in PG(3,Â 9) [i]
  2. linear OOA(9¹², 164, F₉, 3, 6) (dual of [(164, 3), 480, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 12, 164)-net over F₉, using
      - trace code for nets [i] based on digital (0, 6, 82)-net over F₈₁, using
        net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
        Niederreiter sequence [i]
linear OOA(9⁹⁰, 5592402, F₉, 3, 12) (dual of [(5592402, 3), 16777116, 13]-NRT-code), using
- trace code [i] based on linear OOA(81⁴⁵, 2796201, F₈₁, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(81⁴⁵, large, F₈₁, 12) (dual of [large, large−45, 13]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(9¹⁰⁶, 2796323, F₉, 15, 12) (dual of [(2796323, 15), 41944739, 13]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row