MinT - Information on Result #1699272

Information on Result #1699272

Linear OOA(2¹⁵³, 1196, F₂, 8, 25) (dual of [(1196, 8), 9415, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁵³, 1196, F₂, 3, 25) (dual of [(1196, 3), 3435, 26]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁵³, 1376, F₂, 3, 25) (dual of [(1376, 3), 3975, 26]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2¹⁵², 1376, F₂, 3, 25) (dual of [(1376, 3), 3976, 26]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2¹⁵², 4128, F₂, 25) (dual of [4128, 3976, 26]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(2¹⁵¹, 4127, F₂, 25) (dual of [4127, 3976, 26]-code), using
      - constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
        linear OA(2¹⁴⁵, 4097, F₂, 25) (dual of [4097, 3952, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
        linear OA(2¹²¹, 4097, F₂, 21) (dual of [4097, 3976, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
        linear OA(2⁶, 30, F₂, 3) (dual of [30, 24, 4]-code or 30-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

None.