MinT - Information on Result #1599804

Information on Result #1599804

Linear OOA(2²⁴⁹, 913, F₂, 4, 45) (dual of [(913, 4), 3403, 46]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴⁹, 913, F₂, 2, 45) (dual of [(913, 2), 1577, 46]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁴⁹, 1038, F₂, 2, 45) (dual of [(1038, 2), 1827, 46]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2²⁴⁹, 2076, F₂, 45) (dual of [2076, 1827, 46]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁴⁹, 2077, F₂, 45) (dual of [2077, 1828, 46]-code), using
    - constructionÂ X applied to C([0,22]) âŠ‚ C([0,20]) [i] based on
      1. linear OA(2²⁴³, 2049, F₂, 45) (dual of [2049, 1806, 46]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,22], and minimum distance dÂ â‰¥ |{−22,−21,…,22}|+1Â =Â 46 (BCH-bound) [i]
      2. 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]
      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(2²⁴⁹, 456, F₂, 7, 45) (dual of [(456, 7), 2943, 46]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁴⁹, 456, F₂, 8, 45) (dual of [(456, 8), 3399, 46]-NRT-code)	[i]		OOA Folding