MinT - Information on Result #1679580

Information on Result #1679580

Linear OOA(2⁹¹, 77855, F₂, 7, 10) (dual of [(77855, 7), 544894, 11]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁹¹, 77855, F₂, 3, 10) (dual of [(77855, 3), 233474, 11]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁹¹, 87387, F₂, 3, 10) (dual of [(87387, 3), 262070, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2⁹¹, 262161, F₂, 10) (dual of [262161, 262070, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁹¹, 262163, F₂, 10) (dual of [262163, 262072, 11]-code), using
    - 1 times truncation [i] based on linear OA(2⁹², 262164, F₂, 11) (dual of [262164, 262072, 12]-code), using
      - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
        linear OA(2⁹¹, 262144, F₂, 11) (dual of [262144, 262053, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(2⁷³, 262144, F₂, 9) (dual of [262144, 262071, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(2¹⁹, 20, F₂, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
        dual of repetition code with length 20 [i]
        linear OA(2¹, 20, F₂, 1) (dual of [20, 19, 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, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.