MinT - Information on Result #2521580

Information on Result #2521580

Linear OOA(81⁷⁸, large, F₈₁, 2, 9), using 16 times NRT-code embedding in larger space based on linear OOA(81⁴⁶, 8388602, F₈₁, 2, 9) (dual of [(8388602, 2), 16777158, 10]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(81¹³, 4194301, F₈₁, 2, 4) (dual of [(4194301, 2), 8388589, 5]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(81¹³, 8388602, F₈₁, 4) (dual of [8388602, 8388589, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(81¹³, large, F₈₁, 4) (dual of [large, large−13, 5]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
2. linear OOA(81³³, 4194301, F₈₁, 2, 9) (dual of [(4194301, 2), 8388569, 10]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(81³³, 8388602, F₈₁, 9) (dual of [8388602, 8388569, 10]-code), using
    - discarding factors / shortening the dual code based on linear OA(81³³, large, F₈₁, 9) (dual of [large, large−33, 10]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’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 t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(81⁷⁹, large, F₈₁, 2, 9)	[i]		OOA Duplication