MinT - Information on Result #1019348

Information on Result #1019348

Linear OOA(128⁷¹, 2801664, F₁₂₈, 3, 15) (dual of [(2801664, 3), 8404921, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128¹⁴, 5463, F₁₂₈, 3, 7) (dual of [(5463, 3), 16375, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(128¹⁴, 16389, F₁₂₈, 7) (dual of [16389, 16375, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(128¹⁴, 16390, F₁₂₈, 7) (dual of [16390, 16376, 8]-code), using
    - constructionÂ X applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
      1. linear OA(128¹³, 16385, F₁₂₈, 7) (dual of [16385, 16372, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      2. linear OA(128⁹, 16385, F₁₂₈, 5) (dual of [16385, 16376, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’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, 5, F₁₂₈, 1) (dual of [5, 4, 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]
linear OOA(128⁵⁷, 2796201, F₁₂₈, 3, 15) (dual of [(2796201, 3), 8388546, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(128⁵⁷, large, F₁₂₈, 15) (dual of [large, large−57, 16]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]

Mode: Constructive and linear.

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.