MinT - Information on Result #2778428

Information on Result #2778428

Linear OOA(81⁷⁷, large, F₈₁, 4, 7), using strength reduction based on linear OOA(81⁷⁷, large, F₈₁, 4, 11), 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(81⁶⁰, 4194302, F₈₁, 4, 11) (dual of [(4194302, 4), 16777148, 12]-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(81⁴³, 2097151, F₈₁, 4, 11) (dual of [(2097151, 4), 8388561, 12]-NRT-code), using
      - OOA 2-folding [i] based on linear OOA(81⁴³, 4194302, F₈₁, 2, 11) (dual of [(4194302, 2), 8388561, 12]-NRT-code), using
        1 times NRT-code embedding in larger space [i] based on linear OOA(81⁴¹, 4194301, F₈₁, 2, 11) (dual of [(4194301, 2), 8388561, 12]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81⁴¹, 8388602, F₈₁, 11) (dual of [8388602, 8388561, 12]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁴¹, large, F₈₁, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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(81⁷⁸, large, F₈₁, 4, 7)	[i]		OOA Duplication
2	Linear OOA(81⁷⁹, large, F₈₁, 4, 7)	[i]		OOA Duplication