MinT - Information on Result #1749115

Information on Result #1749115

Digital (41, 51, 423)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁵¹, 423, F₂, 2, 10) (dual of [(423, 2), 795, 11]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁵¹, 517, F₂, 2, 10) (dual of [(517, 2), 983, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2⁵¹, 1034, F₂, 10) (dual of [1034, 983, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁵¹, 1035, F₂, 10) (dual of [1035, 984, 11]-code), using
    - 1 times truncation [i] based on linear OA(2⁵², 1036, F₂, 11) (dual of [1036, 984, 12]-code), using
      - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
        linear OA(2⁵¹, 1024, F₂, 11) (dual of [1024, 973, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(2⁴¹, 1024, F₂, 9) (dual of [1024, 983, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(2¹¹, 12, F₂, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,2)), using
        dual of repetition code with length 12 [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.