MinT - Information on Result #1837029

Information on Result #1837029

OOA(128⁶⁶, 3495254, S₁₂₈, 3, 14), using (u,Â u+v)-construction based on

linear OOA(128²⁰, 699053, F₁₂₈, 3, 7) (dual of [(699053, 3), 2097139, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(128²⁰, 2097159, F₁₂₈, 7) (dual of [2097159, 2097139, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(128²⁰, 2097160, F₁₂₈, 7) (dual of [2097160, 2097140, 8]-code), using
    - constructionÂ X applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
      1. linear OA(128¹⁹, 2097153, F₁₂₈, 7) (dual of [2097153, 2097134, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      2. linear OA(128¹³, 2097153, F₁₂₈, 5) (dual of [2097153, 2097140, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
      3. linear OA(128¹, 7, F₁₂₈, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
OOA(128⁴⁶, 2796201, S₁₂₈, 3, 14), using
- OOA 3-folding [i] based on OA(128⁴⁶, large, S₁₂₈, 14), using
  - discarding parts of the base [i] based on linear OA(256⁴⁰, large, F₂₅₆, 14) (dual of [large, large−40, 15]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.