MinT - Information on Result #2226732

Information on Result #2226732

Linear OA(2²⁰³, 16419, F₂, 28) (dual of [16419, 16216, 29]-code), using 1 times truncation based on linear OA(2²⁰⁴, 16420, F₂, 29) (dual of [16420, 16216, 30]-code), using

constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
1. linear OA(2¹⁹⁷, 16385, F₂, 29) (dual of [16385, 16188, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 2²⁸âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
2. linear OA(2¹⁶⁹, 16385, F₂, 25) (dual of [16385, 16216, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 2²⁸âˆ’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, 35, F₂, 3) (dual of [35, 28, 4]-code or 35-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 OA(2²⁰⁵, 16421, F₂, 28) (dual of [16421, 16216, 29]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2²⁰⁶, 16422, F₂, 28) (dual of [16422, 16216, 29]-code)	[i]
3	Linear OA(2²⁰⁷, 16423, F₂, 28) (dual of [16423, 16216, 29]-code)	[i]
4	Linear OOA(2²⁰³, 8209, F₂, 2, 28) (dual of [(8209, 2), 16215, 29]-NRT-code)	[i]	OOA Folding
5	Linear OOA(2²⁰³, 5473, F₂, 3, 28) (dual of [(5473, 3), 16216, 29]-NRT-code)	[i]	OOA Folding