MinT - Information on Result #1748271

Information on Result #1748271

Linear OOA(256²⁸, 32418, F₂₅₆, 18, 13) (dual of [(32418, 18), 583496, 14]-NRT-code), using OOA stacking with additional row based on linear OOA(256²⁸, 32419, F₂₅₆, 6, 13) (dual of [(32419, 6), 194486, 14]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(256²⁸, 32419, F₂₅₆, 2, 13) (dual of [(32419, 2), 64810, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(256²⁸, 32774, F₂₅₆, 2, 13) (dual of [(32774, 2), 65520, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(256²⁸, 65548, F₂₅₆, 13) (dual of [65548, 65520, 14]-code), using
    - constructionÂ X applied to C([0,6]) âŠ‚ C([0,4]) [i] based on
      1. 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]
      2. linear OA(256¹⁷, 65537, F₂₅₆, 9) (dual of [65537, 65520, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
      3. linear OA(256³, 11, F₂₅₆, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
        discarding factors / shortening the dual code based on linear OA(256³, 256, F₂₅₆, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
        Reedâ€“Solomon code RS(253,256) [i]

Mode: 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 (15, 28, 32418)-net over F₂₅₆	[i]		Net Defined by OOA