MinT - Information on Result #1708314

Information on Result #1708314

Digital (46, 57, 686)-net over F₂, using net defined by OOA based on linear OOA(2⁵⁷, 686, F₂, 15, 11) (dual of [(686, 15), 10233, 12]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(2⁵⁷, 687, F₂, 5, 11) (dual of [(687, 5), 3378, 12]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁵⁷, 687, F₂, 3, 11) (dual of [(687, 3), 2004, 12]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2⁵⁷, 2061, F₂, 11) (dual of [2061, 2004, 12]-code), using
    - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
      1. linear OA(2⁵⁶, 2048, F₂, 11) (dual of [2048, 1992, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      2. linear OA(2⁴⁵, 2048, F₂, 9) (dual of [2048, 2003, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      3. linear OA(2¹², 13, F₂, 11) (dual of [13, 1, 12]-code), using
        strength reduction [i] based on linear OA(2¹², 13, F₂, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
        dual of repetition code with length 13 [i]
      4. linear OA(2¹, 13, F₂, 1) (dual of [13, 12, 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.