MinT - Information on Result #1703290

Information on Result #1703290

Linear OOA(2²¹⁴, 2056, F₂, 8, 32) (dual of [(2056, 8), 16234, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹⁴, 2056, F₂, 3, 32) (dual of [(2056, 3), 5954, 33]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²¹⁴, 2741, F₂, 3, 32) (dual of [(2741, 3), 8009, 33]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2²¹⁴, 8223, F₂, 32) (dual of [8223, 8009, 33]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²¹⁴, 8224, F₂, 32) (dual of [8224, 8010, 33]-code), using
    - 1 times truncation [i] based on linear OA(2²¹⁵, 8225, F₂, 33) (dual of [8225, 8010, 34]-code), using
      - constructionÂ X applied to C([0,16]) âŠ‚ C([0,14]) [i] based on
        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(2¹⁸³, 8193, F₂, 29) (dual of [8193, 8010, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (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(2²¹⁴, 1027, F₂, 40, 32) (dual of [(1027, 40), 40866, 33]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row