MinT - Information on Result #1599192

Information on Result #1599192

Linear OOA(2²⁴³, 2269, F₂, 4, 36) (dual of [(2269, 4), 8833, 37]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴³, 2269, F₂, 3, 36) (dual of [(2269, 3), 6564, 37]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁴³, 2742, F₂, 3, 36) (dual of [(2742, 3), 7983, 37]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2²⁴², 2742, F₂, 3, 36) (dual of [(2742, 3), 7984, 37]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2²⁴², 8226, F₂, 36) (dual of [8226, 7984, 37]-code), using
    - 2 times code embedding in larger space [i] based on linear OA(2²⁴⁰, 8224, F₂, 36) (dual of [8224, 7984, 37]-code), using
      - 1 times truncation [i] based on linear OA(2²⁴¹, 8225, F₂, 37) (dual of [8225, 7984, 38]-code), using
        constructionÂ X applied to C([0,18]) âŠ‚ C([0,16]) [i] based on
        linear OA(2²³⁵, 8193, F₂, 37) (dual of [8193, 7958, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
        linear OA(2²⁰⁹, 8193, F₂, 33) (dual of [8193, 7984, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (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(2²⁴³, 1134, F₂, 8, 36) (dual of [(1134, 8), 8829, 37]-NRT-code)	[i]		OOA Folding