MinT - Information on Result #1632423

Information on Result #1632423

Linear OOA(2¹³⁹, 769, F₂, 5, 24) (dual of [(769, 5), 3706, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹³⁹, 769, F₂, 2, 24) (dual of [(769, 2), 1399, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹³⁹, 1038, F₂, 2, 24) (dual of [(1038, 2), 1937, 25]-NRT-code), using
- strength reduction [i] based on linear OOA(2¹³⁹, 1038, F₂, 2, 25) (dual of [(1038, 2), 1937, 26]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹³⁹, 2076, F₂, 25) (dual of [2076, 1937, 26]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹³⁹, 2077, F₂, 25) (dual of [2077, 1938, 26]-code), using
      - constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
        linear OA(2¹³³, 2049, F₂, 25) (dual of [2049, 1916, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
        linear OA(2¹¹¹, 2049, F₂, 21) (dual of [2049, 1938, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
        linear OA(2⁶, 28, F₂, 3) (dual of [28, 22, 4]-code or 28-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.