MinT - Information on Result #1632377

Information on Result #1632377

Linear OOA(2¹³⁸, 2335, F₂, 5, 20) (dual of [(2335, 5), 11537, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹³⁸, 2335, F₂, 3, 20) (dual of [(2335, 3), 6867, 21]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹³⁸, 2742, F₂, 3, 20) (dual of [(2742, 3), 8088, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2¹³⁸, 8226, F₂, 20) (dual of [8226, 8088, 21]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(2¹³⁶, 8224, F₂, 20) (dual of [8224, 8088, 21]-code), using
    - 1 times truncation [i] based on linear OA(2¹³⁷, 8225, F₂, 21) (dual of [8225, 8088, 22]-code), using
      - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
        linear OA(2¹³¹, 8193, F₂, 21) (dual of [8193, 8062, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
        linear OA(2¹⁰⁵, 8193, F₂, 17) (dual of [8193, 8088, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
        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(2¹³⁸, 1167, F₂, 25, 20) (dual of [(1167, 25), 29037, 21]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row