MinT - Information on Result #1204663

Information on Result #1204663

Linear OOA(256³⁸, 9400, F₂₅₆, 15, 15) (dual of [(9400, 15), 140962, 16]-NRT-code), using OOA 7-folding and stacking with additional row based on linear OA(256³⁸, 65801, F₂₅₆, 15) (dual of [65801, 65763, 16]-code), using

discarding factors / shortening the dual code based on linear OA(256³⁸, 65802, F₂₅₆, 15) (dual of [65802, 65764, 16]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(256⁸, 260, F₂₅₆, 7) (dual of [260, 252, 8]-code), using
    - constructionÂ X applied to AG(F, Q+123P) âŠ‚ AG(F, Q+124P) [i] based on
      1. linear OA(256⁷, 257, F₂₅₆, 7) (dual of [257, 250, 8]-code or 257-arc in PG(6,256)), using algebraic-geometric code AG(F, Q+123P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using the rational function field F₂₅₆(x) [i]
      2. linear OA(256⁵, 257, F₂₅₆, 5) (dual of [257, 252, 6]-code or 257-arc in PG(4,256)), using algebraic-geometric code AG(F, Q+124P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257 (see above)
      3. linear OA(256¹, 3, F₂₅₆, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OA(256³⁰, 65542, F₂₅₆, 15) (dual of [65542, 65512, 16]-code), using
    - constructionÂ X applied to C([0,7]) âŠ‚ C([0,6]) [i] based on
      1. linear OA(256²⁹, 65537, F₂₅₆, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
      2. linear OA(256²⁵, 65537, F₂₅₆, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
      3. linear OA(256¹, 5, F₂₅₆, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)

Mode: Constructive and linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (23, 38, 9400)-net over F₂₅₆	[i]		Net Defined by OOA