MinT - Information on Result #1833002

Information on Result #1833002

OOA(32⁷⁰, 8388602, S₃₂, 2, 11), using discarding parts of the base based on linear OOA(64⁵⁸, 8388602, F₆₄, 2, 11) (dual of [(8388602, 2), 16777146, 12]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(64¹⁷, 4194301, F₆₄, 2, 5) (dual of [(4194301, 2), 8388585, 6]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(64¹⁷, 8388602, F₆₄, 5) (dual of [8388602, 8388585, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(64¹⁷, large, F₆₄, 5) (dual of [large, large−17, 6]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’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(64⁴¹, 4194301, F₆₄, 2, 11) (dual of [(4194301, 2), 8388561, 12]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(64⁴¹, 8388602, F₆₄, 11) (dual of [8388602, 8388561, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(64⁴¹, large, F₆₄, 11) (dual of [large, large−41, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive.

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	OOA(32⁷², large, S₃₂, 2, 11)	[i]		NRT-Code Embedding in Larger Space
2	OOA(32⁷⁰, 2796200, S₃₂, 14, 11)	[i]		OOA Folding and Stacking with Additional Row