MinT - Information on Result #1510916

Information on Result #1510916

Linear OOA(2¹¹⁸, 789, F₂, 3, 20) (dual of [(789, 3), 2249, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹¹⁸, 789, F₂, 2, 20) (dual of [(789, 2), 1460, 21]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹¹⁸, 1039, F₂, 2, 20) (dual of [(1039, 2), 1960, 21]-NRT-code), using
- strength reduction [i] based on linear OOA(2¹¹⁸, 1039, F₂, 2, 21) (dual of [(1039, 2), 1960, 22]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹¹⁸, 2078, F₂, 21) (dual of [2078, 1960, 22]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(2¹¹⁷, 2077, F₂, 21) (dual of [2077, 1960, 22]-code), using
      - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
        linear OA(2¹¹¹, 2049, F₂, 21) (dual of [2049, 1938, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
        linear OA(2⁸⁹, 2049, F₂, 17) (dual of [2049, 1960, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
        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(2¹¹⁸, 394, F₂, 6, 20) (dual of [(394, 6), 2246, 21]-NRT-code)	[i]		OOA Folding