MinT - Information on Result #2521679

Information on Result #2521679

Linear OOA(81⁷⁹, large, F₈₁, 2, 13), using 81¹ times duplication based on linear OOA(81⁷⁸, large, F₈₁, 2, 13), using

4 times NRT-code embedding in larger space [i] based on linear OOA(81⁷⁰, 8388602, F₈₁, 2, 13) (dual of [(8388602, 2), 16777134, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81²¹, 4194301, F₈₁, 2, 6) (dual of [(4194301, 2), 8388581, 7]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(81²¹, 8388602, F₈₁, 6) (dual of [8388602, 8388581, 7]-code), using
      - discarding factors / shortening the dual code based on linear OA(81²¹, large, F₈₁, 6) (dual of [large, large−21, 7]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
  2. linear OOA(81⁴⁹, 4194301, F₈₁, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(81⁴⁹, 8388602, F₈₁, 13) (dual of [8388602, 8388553, 14]-code), using
      - discarding factors / shortening the dual code based on linear OA(81⁴⁹, large, F₈₁, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.