MinT - Information on Result #1014312

Information on Result #1014312

Linear OOA(8⁸⁵, 5723477, F₈, 3, 9) (dual of [(5723477, 3), 17170346, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁹, 131075, F₈, 3, 4) (dual of [(131075, 3), 393206, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(8¹⁹, 262150, F₈, 4) (dual of [262150, 262131, 5]-code), using
  - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
    1. linear OA(8¹⁹, 262144, F₈, 4) (dual of [262144, 262125, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
    2. linear OA(8¹³, 262144, F₈, 3) (dual of [262144, 262131, 4]-code or 262144-cap in PG(12,8)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
    3. linear OA(8⁰, 6, F₈, 0) (dual of [6, 6, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 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.