MinT - Information on Result #1053901

Information on Result #1053901

Linear OOA(2²⁵⁰, 8202, F₂, 4, 33) (dual of [(8202, 4), 32558, 34]-NRT-code), using OOA 4-folding based on linear OA(2²⁵⁰, 32808, F₂, 33) (dual of [32808, 32558, 34]-code), using

2 times code embedding in larger space [i] based on linear OA(2²⁴⁸, 32806, F₂, 33) (dual of [32806, 32558, 34]-code), using
- constructionÂ X applied to C([0,16]) âŠ‚ C([0,14]) [i] based on
  1. linear OA(2²⁴¹, 32769, F₂, 33) (dual of [32769, 32528, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 2³⁰âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
  2. linear OA(2²¹¹, 32769, F₂, 29) (dual of [32769, 32558, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 2³⁰âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
  3. linear OA(2⁷, 37, F₂, 3) (dual of [37, 30, 4]-code or 37-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(2²⁵¹, 8202, F₂, 4, 33) (dual of [(8202, 4), 32557, 34]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁵², 8202, F₂, 4, 33) (dual of [(8202, 4), 32556, 34]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁴⁹, 8201, F₂, 4, 32) (dual of [(8201, 4), 32555, 33]-NRT-code)	[i]	Truncation for OOAs