MinT - Information on Result #905323

Information on Result #905323

Linear OOA(128⁷⁸, 8386, F₁₂₈, 2, 30) (dual of [(8386, 2), 16694, 31]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128¹⁸, 192, F₁₂₈, 2, 15) (dual of [(192, 2), 366, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,368P) [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
  - a function field by SÃ©mirat [i]
linear OOA(128⁶⁰, 8194, F₁₂₈, 2, 30) (dual of [(8194, 2), 16328, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁶⁰, 16388, F₁₂₈, 30) (dual of [16388, 16328, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁶⁰, 16389, F₁₂₈, 30) (dual of [16389, 16329, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(27) [i] based on
      1. linear OA(128⁵⁹, 16384, F₁₂₈, 30) (dual of [16384, 16325, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(128⁵⁵, 16384, F₁₂₈, 28) (dual of [16384, 16329, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [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(128⁷⁸, 4193, F₁₂₈, 4, 30) (dual of [(4193, 4), 16694, 31]-NRT-code)	[i]		OOA Folding