MinT - Information on Result #1833136

Information on Result #1833136

OOA(32¹⁰⁸, 4196350, S₃₂, 2, 19), using discarding parts of the base based on linear OOA(64⁹⁰, 4196350, F₆₄, 2, 19) (dual of [(4196350, 2), 8392610, 20]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(64¹⁷, 2049, F₆₄, 2, 9) (dual of [(2049, 2), 4081, 10]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(64¹⁷, 4098, F₆₄, 9) (dual of [4098, 4081, 10]-code), using
    - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
      1. linear OA(64¹⁷, 4096, F₆₄, 9) (dual of [4096, 4079, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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(64⁰, 2, F₆₄, 0) (dual of [2, 2, 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]
2. linear OOA(64⁷³, 4194301, F₆₄, 2, 19) (dual of [(4194301, 2), 8388529, 20]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(64⁷³, 8388602, F₆₄, 19) (dual of [8388602, 8388529, 20]-code), using
    - discarding factors / shortening the dual code based on linear OA(64⁷³, large, F₆₄, 19) (dual of [large, large−73, 20]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

Mode: Constructive.

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.