MinT - Information on Result #2778352

Information on Result #2778352

Linear OOA(81⁷³, large, F₈₁, 4, 6), using strength reduction based on linear OOA(81⁷³, large, F₈₁, 4, 10), using

(u,Â u+v)-construction [i] based on
1. 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]
2. linear OOA(81⁵⁶, 4194302, F₈₁, 4, 10) (dual of [(4194302, 4), 16777152, 11]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(81¹⁷, 4194301, F₈₁, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code) (see above)
    2. linear OOA(81³⁹, 2097151, F₈₁, 4, 10) (dual of [(2097151, 4), 8388565, 11]-NRT-code), using
      - OOA 2-folding [i] based on linear OOA(81³⁹, 4194302, F₈₁, 2, 10) (dual of [(4194302, 2), 8388565, 11]-NRT-code), using
        1 times NRT-code embedding in larger space [i] based on linear OOA(81³⁷, 4194301, F₈₁, 2, 10) (dual of [(4194301, 2), 8388565, 11]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81³⁷, 8388602, F₈₁, 10) (dual of [8388602, 8388565, 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 t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(81⁷⁴, large, F₈₁, 4, 6)	[i]	OOA Duplication
2	Linear OOA(81⁷⁵, large, F₈₁, 4, 6)	[i]
3	Linear OOA(81⁷⁶, large, F₈₁, 4, 6)	[i]