MinT - Information on Result #1750766

Information on Result #1750766

Digital (107, 119, 131078)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹¹⁹, 131078, F₂, 4, 12) (dual of [(131078, 4), 524193, 13]-NRT-code), using

strength reduction [i] based on linear OOA(2¹¹⁹, 131078, F₂, 4, 13) (dual of [(131078, 4), 524193, 14]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹¹⁹, 524312, F₂, 13) (dual of [524312, 524193, 14]-code), using
  - 3 times code embedding in larger space [i] based on linear OA(2¹¹⁶, 524309, F₂, 13) (dual of [524309, 524193, 14]-code), using
    - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [i] based on
      1. linear OA(2¹¹⁵, 524288, F₂, 13) (dual of [524288, 524173, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(2⁹⁶, 524288, F₂, 11) (dual of [524288, 524192, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(2²⁰, 21, F₂, 19) (dual of [21, 1, 20]-code), using
        strength reduction [i] based on linear OA(2²⁰, 21, F₂, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
        dual of repetition code with length 21 [i]
      4. linear OA(2¹, 21, F₂, 1) (dual of [21, 20, 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.