MinT - Information on Result #1753263

Information on Result #1753263

Digital (140, 170, 777)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁷⁰, 777, F₂, 2, 30) (dual of [(777, 2), 1384, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁷⁰, 1031, F₂, 2, 30) (dual of [(1031, 2), 1892, 31]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2¹⁶⁹, 1031, F₂, 2, 30) (dual of [(1031, 2), 1893, 31]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁶⁷, 1030, F₂, 2, 30) (dual of [(1030, 2), 1893, 31]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹⁶⁷, 2060, F₂, 30) (dual of [2060, 1893, 31]-code), using
      - strength reduction [i] based on linear OA(2¹⁶⁷, 2060, F₂, 31) (dual of [2060, 1893, 32]-code), using
        constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
        linear OA(2¹⁶⁶, 2048, F₂, 31) (dual of [2048, 1882, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
        linear OA(2¹⁵⁵, 2048, F₂, 29) (dual of [2048, 1893, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
        linear OA(2¹, 12, F₂, 1) (dual of [12, 11, 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.