MinT - Information on Result #1517226

Information on Result #1517226

Linear OOA(2²²⁶, 921, F₂, 3, 40) (dual of [(921, 3), 2537, 41]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²²⁶, 921, F₂, 2, 40) (dual of [(921, 2), 1616, 41]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²²⁶, 1038, F₂, 2, 40) (dual of [(1038, 2), 1850, 41]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2²²⁶, 2076, F₂, 40) (dual of [2076, 1850, 41]-code), using
  - 1 times truncation [i] based on linear OA(2²²⁷, 2077, F₂, 41) (dual of [2077, 1850, 42]-code), using
    - constructionÂ X applied to C([0,20]) âŠ‚ C([0,18]) [i] based on
      1. linear OA(2²²¹, 2049, F₂, 41) (dual of [2049, 1828, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,20], and minimum distance dÂ â‰¥ |{−20,−19,…,20}|+1Â =Â 42 (BCH-bound) [i]
      2. linear OA(2¹⁹⁹, 2049, F₂, 37) (dual of [2049, 1850, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
      3. linear OA(2⁶, 28, F₂, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
        discarding factors / shortening the dual code based on linear OA(2⁶, 32, F₂, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
        Reedâ€“Muller code RM(1,5) [i]
        caps in base bÂ =Â 2 [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(2²²⁶, 460, F₂, 5, 40) (dual of [(460, 5), 2074, 41]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²²⁶, 460, F₂, 6, 40) (dual of [(460, 6), 2534, 41]-NRT-code)	[i]		OOA Folding