MinT - Information on Result #1019264

Information on Result #1019264

Linear OOA(128³³, 5613, F₁₂₈, 3, 13) (dual of [(5613, 3), 16806, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128⁷, 150, F₁₂₈, 3, 6) (dual of [(150, 3), 443, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,443P) [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(128²⁶, 5463, F₁₂₈, 3, 13) (dual of [(5463, 3), 16363, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(128²⁶, 16389, F₁₂₈, 13) (dual of [16389, 16363, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(128²⁶, 16390, F₁₂₈, 13) (dual of [16390, 16364, 14]-code), using
    - constructionÂ X applied to C([0,6]) âŠ‚ C([0,5]) [i] based on
      1. linear OA(128²⁵, 16385, F₁₂₈, 13) (dual of [16385, 16360, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
      2. linear OA(128²¹, 16385, F₁₂₈, 11) (dual of [16385, 16364, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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(128³³, 2806, F₁₂₈, 15, 13) (dual of [(2806, 15), 42057, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row