MinT - Information on Result #1068677

Information on Result #1068677

Linear OOA(81⁵⁸, 4194301, F₈₁, 4, 11) (dual of [(4194301, 4), 16777146, 12]-NRT-code), using OOA 2-folding based on linear OOA(81⁵⁸, 8388602, F₈₁, 2, 11) (dual of [(8388602, 2), 16777146, 12]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(81¹⁷, 4194301, F₈₁, 2, 5) (dual of [(4194301, 2), 8388585, 6]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(81¹⁷, 8388602, F₈₁, 5) (dual of [8388602, 8388585, 6]-code), using
    - discarding factors / shortening the dual code 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(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 s, k and t, m and s, 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(81⁵⁹, 4194301, F₈₁, 4, 11) (dual of [(4194301, 4), 16777145, 12]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(81⁷⁵, 8388602, F₈₁, 4, 11) (dual of [(8388602, 4), 33554333, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs