MinT - Information on Result #1070584

Information on Result #1070584

Linear OOA(128⁵³, 4172, F₁₂₈, 4, 21) (dual of [(4172, 4), 16635, 22]-NRT-code), using OOA 2-folding based on linear OOA(128⁵³, 8344, F₁₂₈, 2, 21) (dual of [(8344, 2), 16635, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁵³, 8345, F₁₂₈, 2, 21) (dual of [(8345, 2), 16637, 22]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128¹¹, 150, F₁₂₈, 2, 10) (dual of [(150, 2), 289, 11]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,289P) [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]
  2. linear OOA(128⁴², 8195, F₁₂₈, 2, 21) (dual of [(8195, 2), 16348, 22]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(128⁴², 16390, F₁₂₈, 21) (dual of [16390, 16348, 22]-code), using
      - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
        linear OA(128⁴¹, 16385, F₁₂₈, 21) (dual of [16385, 16344, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
        linear OA(128³⁷, 16385, F₁₂₈, 19) (dual of [16385, 16348, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
        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]

Mode: Constructive and linear.

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.