MinT - Information on Result #1070185

Information on Result #1070185

Linear OOA(128³⁰, 4171, F₁₂₈, 4, 12) (dual of [(4171, 4), 16654, 13]-NRT-code), using OOA 2-folding based on linear OOA(128³⁰, 8342, F₁₂₈, 2, 12) (dual of [(8342, 2), 16654, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128³⁰, 8343, F₁₂₈, 2, 12) (dual of [(8343, 2), 16656, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128⁷, 150, F₁₂₈, 2, 6) (dual of [(150, 2), 293, 7]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,293P) [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(128²³, 8193, F₁₂₈, 2, 12) (dual of [(8193, 2), 16363, 13]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(128²³, 16386, F₁₂₈, 12) (dual of [16386, 16363, 13]-code), using
      - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
        linear OA(128²³, 16384, F₁₂₈, 12) (dual of [16384, 16361, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(128²¹, 16384, F₁₂₈, 11) (dual of [16384, 16363, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.