MinT - Information on Result #1083206

Information on Result #1083206

Linear OOA(128⁴³, 4247, F₁₂₈, 4, 17) (dual of [(4247, 4), 16945, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128⁹, 150, F₁₂₈, 4, 8) (dual of [(150, 4), 591, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,591P) [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(128³⁴, 4097, F₁₂₈, 4, 17) (dual of [(4097, 4), 16354, 18]-NRT-code), using
- OOA 4-folding [i] based on linear OA(128³⁴, 16388, F₁₂₈, 17) (dual of [16388, 16354, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(128³⁴, 16390, F₁₂₈, 17) (dual of [16390, 16356, 18]-code), using
    - constructionÂ X applied to C([0,8]) âŠ‚ C([0,7]) [i] based on
      1. linear OA(128³³, 16385, F₁₂₈, 17) (dual of [16385, 16352, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      2. linear OA(128²⁹, 16385, F₁₂₈, 15) (dual of [16385, 16356, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (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]

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(128⁴³, 2123, F₁₂₈, 20, 17) (dual of [(2123, 20), 42417, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row