MinT - Information on Result #1697346

Information on Result #1697346

Linear OOA(2¹¹⁰, 8197, F₂, 8, 14) (dual of [(8197, 8), 65466, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹¹⁰, 8197, F₂, 4, 14) (dual of [(8197, 4), 32678, 15]-NRT-code), using

strength reduction [i] based on linear OOA(2¹¹⁰, 8197, F₂, 4, 15) (dual of [(8197, 4), 32678, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹¹⁰, 32788, F₂, 15) (dual of [32788, 32678, 16]-code), using
  - 3 times code embedding in larger space [i] based on linear OA(2¹⁰⁷, 32785, F₂, 15) (dual of [32785, 32678, 16]-code), using
    - constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
      1. linear OA(2¹⁰⁶, 32768, F₂, 15) (dual of [32768, 32662, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      2. linear OA(2⁹¹, 32768, F₂, 13) (dual of [32768, 32677, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(2¹⁶, 17, F₂, 15) (dual of [17, 1, 16]-code), using
        strength reduction [i] based on linear OA(2¹⁶, 17, F₂, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
        dual of repetition code with length 17 [i]
      4. linear OA(2¹, 17, F₂, 1) (dual of [17, 16, 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.