MinT - Information on Result #2806743

Information on Result #2806743

Linear OOA(81⁷⁹, 4194301, F₈₁, 4, 14) (dual of [(4194301, 4), 16777125, 15]-NRT-code), using 81¹ times duplication based on linear OOA(81⁷⁸, 4194301, F₈₁, 4, 14) (dual of [(4194301, 4), 16777126, 15]-NRT-code), using

OOA 2-folding [i] based on linear OOA(81⁷⁸, 8388602, F₈₁, 2, 14) (dual of [(8388602, 2), 16777126, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81²⁵, 4194301, F₈₁, 2, 7) (dual of [(4194301, 2), 8388577, 8]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(81²⁵, 8388602, F₈₁, 7) (dual of [8388602, 8388577, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(81²⁵, large, F₈₁, 7) (dual of [large, large−25, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
  2. linear OOA(81⁵³, 4194301, F₈₁, 2, 14) (dual of [(4194301, 2), 8388549, 15]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(81⁵³, 8388602, F₈₁, 14) (dual of [8388602, 8388549, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(81⁵³, large, F₈₁, 14) (dual of [large, large−53, 15]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.