MinT - Information on Result #1084806

Information on Result #1084806

Linear OOA(81⁵⁹, 4210618, F₈₁, 4, 10) (dual of [(4210618, 4), 16842413, 11]-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(81³⁷, 2097150, F₈₁, 4, 10) (dual of [(2097150, 4), 8388563, 11]-NRT-code), using
- OOA 4-folding [i] based on linear OA(81³⁷, 8388600, F₈₁, 10) (dual of [8388600, 8388563, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(81³⁷, large, F₈₁, 10) (dual of [large, large−37, 11]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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.