MinT - Information on Result #1567304

Information on Result #1567304

Linear OOA(256²⁸, 32419, F₂₅₆, 3, 13) (dual of [(32419, 3), 97229, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound 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.

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(256²⁸, 16209, F₂₅₆, 5, 13) (dual of [(16209, 5), 81017, 14]-NRT-code)	[i]		OOA Folding
2	Linear OOA(256²⁸, 16209, F₂₅₆, 6, 13) (dual of [(16209, 6), 97226, 14]-NRT-code)	[i]		OOA Folding