MinT - Information on Result #1831705

Information on Result #1831705

OOA(27⁴², 9925, S₂₇, 2, 12), using (u,Â u+v)-construction based on

OOA(27⁸, 82, S₂₇, 2, 6), using
- extracting embedded OOA [i] based on (2, 8, 82)-net in base 27, using
  - base change [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(27³⁴, 9843, F₂₇, 2, 12) (dual of [(9843, 2), 19652, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27³⁴, 19686, F₂₇, 12) (dual of [19686, 19652, 13]-code), using
  - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
    1. linear OA(27³⁴, 19683, F₂₇, 12) (dual of [19683, 19649, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    2. linear OA(27³¹, 19683, F₂₇, 11) (dual of [19683, 19652, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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.