MinT - Information on Result #904476

Information on Result #904476

Linear OOA(81⁸², 8388602, F₈₁, 2, 15) (dual of [(8388602, 2), 16777122, 16]-NRT-code), using (u,Â u+v)-construction based on

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]
linear OOA(81⁵⁷, 4194301, F₈₁, 2, 15) (dual of [(4194301, 2), 8388545, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81⁵⁷, 8388602, F₈₁, 15) (dual of [8388602, 8388545, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁵⁷, large, F₈₁, 15) (dual of [large, large−57, 16]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(81⁸², 4194301, F₈₁, 3, 15) (dual of [(4194301, 3), 12582821, 16]-NRT-code)	[i]	OOA Folding
2	Linear OOA(81⁸², 4194301, F₈₁, 4, 15) (dual of [(4194301, 4), 16777122, 16]-NRT-code)	[i]	OOA Folding
3	Linear OOA(81⁸², 2097150, F₈₁, 18, 15) (dual of [(2097150, 18), 37748618, 16]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row