MinT - Information on Result #1752469

Information on Result #1752469

Digital (129, 156, 803)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁵⁶, 803, F₂, 2, 27) (dual of [(803, 2), 1450, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁵⁶, 1046, F₂, 2, 27) (dual of [(1046, 2), 1936, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹⁵⁶, 2092, F₂, 27) (dual of [2092, 1936, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁵⁶, 2093, F₂, 27) (dual of [2093, 1937, 28]-code), using
    - constructionÂ X applied to C_e(26) âŠ‚ C_e(20) [i] based on
      1. linear OA(2¹⁴⁴, 2048, F₂, 27) (dual of [2048, 1904, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      2. linear OA(2¹¹¹, 2048, F₂, 21) (dual of [2048, 1937, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. linear OA(2¹², 45, F₂, 5) (dual of [45, 33, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹², 48, F₂, 5) (dual of [48, 36, 6]-code), using
        adding a parity check bit [i] based on linear OA(2¹¹, 47, F₂, 4) (dual of [47, 36, 5]-code), using
        extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F₂, using
        linear code embedding found in a computer search [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.