MinT - Information on Result #2526619

Information on Result #2526619

OOA(27¹¹⁰, 9961, S₂₇, 2, 30), using 27¹ times duplication based on OOA(27¹⁰⁹, 9961, S₂₇, 2, 30), using

(u,Â u+v)-construction [i] based on
1. OOA(27²³, 116, S₂₇, 2, 15), using
  - extracting embedded OOA [i] based on (8, 23, 116)-net in base 27, using
    - 1 times m-reduction [i] based on (8, 24, 116)-net in base 27, using
      - base change [i] based on digital (2, 18, 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]
2. linear OOA(27⁸⁶, 9845, F₂₇, 2, 30) (dual of [(9845, 2), 19604, 31]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(27⁸⁶, 19690, F₂₇, 30) (dual of [19690, 19604, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(27) [i] based on
      1. linear OA(27⁸⁵, 19683, F₂₇, 30) (dual of [19683, 19598, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(27⁷⁹, 19683, F₂₇, 28) (dual of [19683, 19604, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      3. linear OA(27¹, 7, F₂₇, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(27¹, s, F₂₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.