MinT - Information on Result #1494677

Information on Result #1494677

Linear OOA(64³², 1942, F₆₄, 3, 14) (dual of [(1942, 3), 5794, 15]-NRT-code), using OOA 2-folding based on linear OOA(64³², 3884, F₆₄, 2, 14) (dual of [(3884, 2), 7736, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(64³², 3885, F₆₄, 2, 14) (dual of [(3885, 2), 7738, 15]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(64³², 3885, F₆₄, 14) (dual of [3885, 3853, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(64³², 4113, F₆₄, 14) (dual of [4113, 4081, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(7) [i] based on
      1. linear OA(64²⁷, 4096, F₆₄, 14) (dual of [4096, 4069, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      2. linear OA(64¹⁵, 4096, F₆₄, 8) (dual of [4096, 4081, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. linear OA(64⁵, 17, F₆₄, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,64)), using
        discarding factors / shortening the dual code based on linear OA(64⁵, 64, F₆₄, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
        Reedâ€“Solomon code RS(59,64) [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.