MinT - Information on Result #1831787

Information on Result #1831787

OOA(27⁷⁰, 9959, S₂₇, 2, 19), using (u,Â u+v)-construction based on

OOA(27¹⁵, 116, S₂₇, 2, 9), using
- extracting embedded OOA [i] based on (6, 15, 116)-net in base 27, using
  - 1 times m-reduction [i] based on (6, 16, 116)-net in base 27, using
    - base change [i] based on digital (2, 12, 116)-net over F₈₁, using
      - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]
linear OOA(27⁵⁵, 9843, F₂₇, 2, 19) (dual of [(9843, 2), 19631, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27⁵⁵, 19686, F₂₇, 19) (dual of [19686, 19631, 20]-code), using
  - constructionÂ X applied to C_e(18) âŠ‚ C_e(17) [i] based on
    1. linear OA(27⁵⁵, 19683, F₂₇, 19) (dual of [19683, 19628, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    2. linear OA(27⁵², 19683, F₂₇, 18) (dual of [19683, 19631, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    3. linear OA(27⁰, 3, F₂₇, 0) (dual of [3, 3, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.