MinT - Information on Result #2523028

Information on Result #2523028

OOA(2¹⁷⁴, 4196355, S₂, 2, 12), using strength reduction based on OOA(2¹⁷⁴, 4196355, S₂, 2, 13), using

(u,Â u+v)-construction [i] based on
1. OOA(2³⁵, 2054, S₂, 2, 6), using
  - OOA 2-folding [i] based on OA(2³⁵, 4108, S₂, 6), using
    - 1 times truncation [i] based on OA(2³⁶, 4109, S₂, 7), using
      - constructionÂ X4 applied to K(12) âŠ‚ DG(12,5) [i] based on
        OA(2³⁵, 4096, S₂, 7), using Delsarteâ€“Goethals OA DG(12,5) [i]
        OA(2²⁴, 4096, S₂, 5), using Kerdock OA K(12) [i]
        linear OA(2¹², 13, F₂, 11) (dual of [13, 1, 12]-code), using
        strength reduction [i] based on linear OA(2¹², 13, F₂, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
        dual of repetition code with length 13 [i]
        linear OA(2¹, 13, F₂, 1) (dual of [13, 12, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OOA(2¹³⁹, 4194301, F₂, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹³⁹, 8388602, F₂, 13) (dual of [8388602, 8388463, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive.

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.