MinT - Information on Result #1592656

Information on Result #1592656

Linear OOA(2¹⁶², 714, F₂, 4, 29) (dual of [(714, 4), 2694, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁶², 714, F₂, 2, 29) (dual of [(714, 2), 1266, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁶², 1039, F₂, 2, 29) (dual of [(1039, 2), 1916, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹⁶², 2078, F₂, 29) (dual of [2078, 1916, 30]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(2¹⁶¹, 2077, F₂, 29) (dual of [2077, 1916, 30]-code), using
    - constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
      1. linear OA(2¹⁵⁵, 2049, F₂, 29) (dual of [2049, 1894, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
      2. linear OA(2¹³³, 2049, F₂, 25) (dual of [2049, 1916, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (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(2¹⁶², 357, F₂, 7, 29) (dual of [(357, 7), 2337, 30]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁶², 357, F₂, 8, 29) (dual of [(357, 8), 2694, 30]-NRT-code)	[i]		OOA Folding