MinT - Information on Result #1017965

Information on Result #1017965

Linear OOA(64⁸⁷, 2883583, F₆₄, 3, 17) (dual of [(2883583, 3), 8650662, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64²², 87382, F₆₄, 3, 8) (dual of [(87382, 3), 262124, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64²², 262146, F₆₄, 8) (dual of [262146, 262124, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(64²², 262147, F₆₄, 8) (dual of [262147, 262125, 9]-code), using
    - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
      1. linear OA(64²², 262144, F₆₄, 8) (dual of [262144, 262122, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      2. linear OA(64¹⁹, 262144, F₆₄, 7) (dual of [262144, 262125, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
linear OOA(64⁶⁵, 2796201, F₆₄, 3, 17) (dual of [(2796201, 3), 8388538, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64⁶⁵, large, F₆₄, 17) (dual of [large, large−65, 18]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: Constructive and 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.