MinT - Information on Result #947067

Information on Result #947067

Linear OOA(2²⁴⁷, 43705, F₂, 3, 29) (dual of [(43705, 3), 130868, 30]-NRT-code), using OOA 3-folding based on linear OA(2²⁴⁷, 131115, F₂, 29) (dual of [131115, 130868, 30]-code), using

1 times code embedding in larger space [i] based on linear OA(2²⁴⁶, 131114, F₂, 29) (dual of [131114, 130868, 30]-code), using
- constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
  1. linear OA(2²³⁹, 131073, F₂, 29) (dual of [131073, 130834, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073Â | 2³⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
  2. linear OA(2²⁰⁵, 131073, F₂, 25) (dual of [131073, 130868, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073Â | 2³⁴âˆ’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, 41, F₂, 3) (dual of [41, 34, 4]-code or 41-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(2²⁵⁰, 43706, F₂, 3, 29) (dual of [(43706, 3), 130868, 30]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁴⁸, 43705, F₂, 3, 29) (dual of [(43705, 3), 130867, 30]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁴⁹, 43705, F₂, 3, 29) (dual of [(43705, 3), 130866, 30]-NRT-code)	[i]	OOA Duplication