MinT - Information on Result #1757653

Information on Result #1757653

Digital (191, 231, 1016)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³¹, 1016, F₂, 2, 40) (dual of [(1016, 2), 1801, 41]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³¹, 1042, F₂, 2, 40) (dual of [(1042, 2), 1853, 41]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2²³¹, 2084, F₂, 40) (dual of [2084, 1853, 41]-code), using
  - 1 times truncation [i] based on linear OA(2²³², 2085, F₂, 41) (dual of [2085, 1853, 42]-code), using
    - constructionÂ XX applied to C_e(40) âŠ‚ C_e(36) âŠ‚ C_e(34) [i] based on
      1. linear OA(2²²¹, 2048, F₂, 41) (dual of [2048, 1827, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
      2. linear OA(2¹⁹⁹, 2048, F₂, 37) (dual of [2048, 1849, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
      3. linear OA(2¹⁸⁸, 2048, F₂, 35) (dual of [2048, 1860, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
      4. 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]
      5. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.