MinT - Information on Result #1832993

Information on Result #1832993

OOA(32⁶⁵, 8388602, S₃₂, 2, 10), using discarding parts of the base based on linear OOA(64⁵⁴, 8388602, F₆₄, 2, 10) (dual of [(8388602, 2), 16777150, 11]-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(64³⁷, 4194301, F₆₄, 2, 10) (dual of [(4194301, 2), 8388565, 11]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(64³⁷, 8388602, F₆₄, 10) (dual of [8388602, 8388565, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(64³⁷, large, F₆₄, 10) (dual of [large, large−37, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(32⁶⁷, large, S₃₂, 2, 10)	[i]		NRT-Code Embedding in Larger Space
2	OOA(32⁶⁵, 2796200, S₃₂, 14, 10)	[i]		OOA Folding and Stacking with Additional Row