MinT - Information on Result #2522288

Information on Result #2522288

Linear OOA(128⁷⁰, large, F₁₂₈, 2, 11), using 6 times NRT-code embedding in larger space based on linear OOA(128⁵⁸, 8388602, F₁₂₈, 2, 11) (dual of [(8388602, 2), 16777146, 12]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(128¹⁷, 4194301, F₁₂₈, 2, 5) (dual of [(4194301, 2), 8388585, 6]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(128¹⁷, 8388602, F₁₂₈, 5) (dual of [8388602, 8388585, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(128¹⁷, large, F₁₂₈, 5) (dual of [large, large−17, 6]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 17895697Â | 128⁴âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
2. linear OOA(128⁴¹, 4194301, F₁₂₈, 2, 11) (dual of [(4194301, 2), 8388561, 12]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(128⁴¹, 8388602, F₁₂₈, 11) (dual of [8388602, 8388561, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(128⁴¹, large, F₁₂₈, 11) (dual of [large, large−41, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’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(128⁷¹, large, F₁₂₈, 2, 11)	[i]		OOA Duplication