MinT - Information on Result #905112

Information on Result #905112

Linear OOA(128⁵¹, 8344, F₁₂₈, 2, 20) (dual of [(8344, 2), 16637, 21]-NRT-code), using (u,Â u+v)-construction based on

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]
linear OOA(128⁴⁰, 8194, F₁₂₈, 2, 20) (dual of [(8194, 2), 16348, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁴⁰, 16388, F₁₂₈, 20) (dual of [16388, 16348, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁴⁰, 16389, F₁₂₈, 20) (dual of [16389, 16349, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(17) [i] based on
      1. linear OA(128³⁹, 16384, F₁₂₈, 20) (dual of [16384, 16345, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(128³⁵, 16384, F₁₂₈, 18) (dual of [16384, 16349, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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]

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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(128⁵¹, 4172, F₁₂₈, 4, 20) (dual of [(4172, 4), 16637, 21]-NRT-code)	[i]		OOA Folding