MinT - Information on Result #1753086

Information on Result #1753086

Digital (138, 167, 821)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁶⁷, 821, F₂, 2, 29) (dual of [(821, 2), 1475, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁶⁷, 1046, F₂, 2, 29) (dual of [(1046, 2), 1925, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹⁶⁷, 2092, F₂, 29) (dual of [2092, 1925, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁶⁷, 2093, F₂, 29) (dual of [2093, 1926, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(22) [i] based on
      1. 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]
      2. linear OA(2¹²², 2048, F₂, 23) (dual of [2048, 1926, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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.