MinT - Information on Result #2619426

Information on Result #2619426

Linear OOA(2²⁵⁰, 349542, F₂, 3, 24) (dual of [(349542, 3), 1048376, 25]-NRT-code), using strength reduction based on linear OOA(2²⁵⁰, 349542, F₂, 3, 25) (dual of [(349542, 3), 1048376, 26]-NRT-code), using

OOA 3-folding [i] based on linear OA(2²⁵⁰, 1048626, F₂, 25) (dual of [1048626, 1048376, 26]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2²⁴⁸, 1048624, F₂, 25) (dual of [1048624, 1048376, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
    1. linear OA(2²⁴¹, 1048577, F₂, 25) (dual of [1048577, 1048336, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 2⁴⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    2. linear OA(2²⁰¹, 1048577, F₂, 21) (dual of [1048577, 1048376, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 2⁴⁰âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
    3. linear OA(2⁷, 47, F₂, 3) (dual of [47, 40, 4]-code or 47-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		This result only	Method
1	Linear OOA(2²⁵¹, 349542, F₂, 3, 24) (dual of [(349542, 3), 1048375, 25]-NRT-code)	[i]		OOA Duplication