MinT - Information on Result #1697498

Information on Result #1697498

Linear OOA(2¹¹⁴, 1109874, F₂, 8, 10) (dual of [(1109874, 8), 8878878, 11]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹¹⁴, 1109874, F₂, 3, 10) (dual of [(1109874, 3), 3329508, 11]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹¹⁴, 1398110, F₂, 3, 10) (dual of [(1398110, 3), 4194216, 11]-NRT-code), using
- strength reduction [i] based on linear OOA(2¹¹⁴, 1398110, F₂, 3, 11) (dual of [(1398110, 3), 4194216, 12]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2¹¹⁴, 4194330, F₂, 11) (dual of [4194330, 4194216, 12]-code), using
    - 2 times code embedding in larger space [i] based on linear OA(2¹¹², 4194328, F₂, 11) (dual of [4194328, 4194216, 12]-code), using
      - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
        linear OA(2¹¹¹, 4194304, F₂, 11) (dual of [4194304, 4194193, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 2²²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(2⁸⁹, 4194304, F₂, 9) (dual of [4194304, 4194215, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 2²²âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(2²³, 24, F₂, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
        dual of repetition code with length 24 [i]
        linear OA(2¹, 24, F₂, 1) (dual of [24, 23, 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.

Other Results with Identical Parameters

None.

Depending Results

None.