MinT - Information on Result #2186809

Information on Result #2186809

Linear OA(2²³², 65576, F₂, 28) (dual of [65576, 65344, 29]-code), using strength reduction based on linear OA(2²³², 65576, F₂, 29) (dual of [65576, 65344, 30]-code), using

constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
1. linear OA(2²²⁵, 65537, F₂, 29) (dual of [65537, 65312, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
2. linear OA(2¹⁹³, 65537, F₂, 25) (dual of [65537, 65344, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
3. linear OA(2⁷, 39, F₂, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
  - discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2²³², 32788, F₂, 2, 28) (dual of [(32788, 2), 65344, 29]-NRT-code)	[i]	OOA Folding
2	Linear OOA(2²³², 16394, F₂, 4, 28) (dual of [(16394, 4), 65344, 29]-NRT-code)	[i]
3	Linear OOA(2²³², 9368, F₂, 7, 28) (dual of [(9368, 7), 65344, 29]-NRT-code)	[i]
4	Linear OOA(2²³², 8197, F₂, 8, 28) (dual of [(8197, 8), 65344, 29]-NRT-code)	[i]
5	Linear OOA(2²³², 4684, F₂, 28, 28) (dual of [(4684, 28), 130920, 29]-NRT-code)	[i]	OA Folding and Stacking