MinT - Information on Result #1151901

Information on Result #1151901

Linear OOA(2²⁰⁶, 18727, F₂, 7, 25) (dual of [(18727, 7), 130883, 26]-NRT-code), using OOA 7-folding based on linear OA(2²⁰⁶, 131089, F₂, 25) (dual of [131089, 130883, 26]-code), using

discarding factors / shortening the dual code based on linear OA(2²⁰⁶, 131090, F₂, 25) (dual of [131090, 130884, 26]-code), using
- constructionÂ X applied to C_e(24) âŠ‚ C_e(22) [i] based on
  1. linear OA(2²⁰⁵, 131072, F₂, 25) (dual of [131072, 130867, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
  2. linear OA(2¹⁸⁸, 131072, F₂, 23) (dual of [131072, 130884, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  3. linear OA(2¹, 18, F₂, 1) (dual of [18, 17, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [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(2²⁰⁶, 18727, F₂, 7, 24) (dual of [(18727, 7), 130883, 25]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁰⁷, 18727, F₂, 7, 25) (dual of [(18727, 7), 130882, 26]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰⁸, 18727, F₂, 7, 25) (dual of [(18727, 7), 130881, 26]-NRT-code)	[i]
4	Linear OOA(2²⁰⁹, 18727, F₂, 7, 25) (dual of [(18727, 7), 130880, 26]-NRT-code)	[i]
5	Linear OOA(2²¹⁰, 18727, F₂, 7, 25) (dual of [(18727, 7), 130879, 26]-NRT-code)	[i]
6	Linear OOA(2²⁰⁶, 18727, F₂, 8, 25) (dual of [(18727, 8), 149610, 26]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
7	Digital (181, 206, 18727)-net over F₂	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound