MinT - Information on Result #1079228

Information on Result #1079228

Linear OOA(3¹⁷², large, F₃, 4, 11), using trace code based on 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		Method
1	Linear OOA(3¹⁷², large, F₃, 4, 10)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹⁷², large, F₃, 4, 9)	[i]
3	Linear OOA(3¹⁷², large, F₃, 4, 8)	[i]
4	Linear OOA(3¹⁷², large, F₃, 4, 7)	[i]
5	Linear OOA(3¹⁷², large, F₃, 4, 6)	[i]
6	Linear OOA(3¹⁷², large, F₃, 4, 5)	[i]
7	Linear OOA(3¹⁷², large, F₃, 4, 4)	[i]
8	Linear OOA(3¹⁷², large, F₃, 4, 3)	[i]