MinT - Information on Result #1667723

Information on Result #1667723

Linear OOA(2¹⁹⁸, 12734, F₂, 6, 24) (dual of [(12734, 6), 76206, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹⁸, 12734, F₂, 5, 24) (dual of [(12734, 5), 63472, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁹⁸, 13113, F₂, 5, 24) (dual of [(13113, 5), 65367, 25]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2¹⁹⁸, 65565, F₂, 24) (dual of [65565, 65367, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁹⁸, 65568, F₂, 24) (dual of [65568, 65370, 25]-code), using
    - 1 times truncation [i] based on linear OA(2¹⁹⁹, 65569, F₂, 25) (dual of [65569, 65370, 26]-code), using
      - constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
        linear OA(2¹⁹³, 65537, F₂, 25) (dual of [65537, 65344, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
        linear OA(2¹⁶¹, 65537, F₂, 21) (dual of [65537, 65376, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (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(2¹⁹⁸, 6366, F₂, 30, 24) (dual of [(6366, 30), 190782, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row