MinT - Information on Result #1751910

Information on Result #1751910

Digital (130, 145, 199716)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁴⁵, 199716, F₂, 5, 15) (dual of [(199716, 5), 998435, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁴⁵, 209720, F₂, 5, 15) (dual of [(209720, 5), 1048455, 16]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2¹⁴⁴, 209720, F₂, 5, 15) (dual of [(209720, 5), 1048456, 16]-NRT-code), using
  - OOA 5-folding [i] based on linear OA(2¹⁴⁴, 1048600, F₂, 15) (dual of [1048600, 1048456, 16]-code), using
    - 2 times code embedding in larger space [i] based on linear OA(2¹⁴², 1048598, F₂, 15) (dual of [1048598, 1048456, 16]-code), using
      - constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
        linear OA(2¹⁴¹, 1048576, F₂, 15) (dual of [1048576, 1048435, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(2¹²¹, 1048576, F₂, 13) (dual of [1048576, 1048455, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(2²¹, 22, F₂, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,2)), using
        dual of repetition code with length 22 [i]
        linear OA(2¹, 22, F₂, 1) (dual of [22, 21, 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.