MinT - Information on Result #1084802

Information on Result #1084802

Linear OOA(81⁶³, 4210618, F₈₁, 4, 11) (dual of [(4210618, 4), 16842409, 12]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(81⁵, 16318, F₈₁, 4, 3) (dual of [(16318, 4), 65267, 4]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(81⁵, 16318, F₈₁, 3, 3) (dual of [(16318, 3), 48949, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(81⁵, 16318, F₈₁, 2, 3) (dual of [(16318, 2), 32631, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(81⁵, 16318, F₈₁, 3) (dual of [16318, 16313, 4]-code or 16318-cap in PG(4,81)), using
      - large caps in PG(4,Â b) [i]
linear OOA(81¹⁷, 2097150, F₈₁, 4, 5) (dual of [(2097150, 4), 8388583, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81¹⁷, 4194301, F₈₁, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(81¹⁷, large, F₈₁, 5) (dual of [large, large−17, 6]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
linear OOA(81⁴¹, 2097150, F₈₁, 4, 11) (dual of [(2097150, 4), 8388559, 12]-NRT-code), using
- OOA 4-folding [i] based on linear OA(81⁴¹, 8388600, F₈₁, 11) (dual of [8388600, 8388559, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁴¹, large, F₈₁, 11) (dual of [large, large−41, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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.