MinT - Information on Result #1014307

Information on Result #1014307

Linear OOA(8⁸⁰, 5596500, F₈, 3, 9) (dual of [(5596500, 3), 16789420, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁴, 4098, F₈, 3, 4) (dual of [(4098, 3), 12280, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(8¹⁴, 8196, F₈, 4) (dual of [8196, 8182, 5]-code), using
  - trace code [i] based on linear OA(64⁷, 4098, F₆₄, 4) (dual of [4098, 4091, 5]-code), using
    - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
      1. linear OA(64⁷, 4096, F₆₄, 4) (dual of [4096, 4089, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      2. linear OA(64⁵, 4096, F₆₄, 3) (dual of [4096, 4091, 4]-code or 4096-cap in PG(4,64)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [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]
linear OOA(8⁶⁶, 5592402, F₈, 3, 9) (dual of [(5592402, 3), 16777140, 10]-NRT-code), using
- trace code [i] based on linear OOA(64³³, 2796201, F₆₄, 3, 9) (dual of [(2796201, 3), 8388570, 10]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(64³³, large, F₆₄, 9) (dual of [large, large−33, 10]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (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.