MinT - Information on Result #1152072

Information on Result #1152072

Linear OOA(2²⁰³, 4686, F₂, 7, 27) (dual of [(4686, 7), 32599, 28]-NRT-code), using OOA 7-folding based on linear OA(2²⁰³, 32802, F₂, 27) (dual of [32802, 32599, 28]-code), using

discarding factors / shortening the dual code based on linear OA(2²⁰³, 32805, F₂, 27) (dual of [32805, 32602, 28]-code), using
- constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
  1. linear OA(2¹⁹⁶, 32768, F₂, 27) (dual of [32768, 32572, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
  2. linear OA(2¹⁶⁶, 32768, F₂, 23) (dual of [32768, 32602, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(2²⁰³, 4686, F₂, 7, 26) (dual of [(4686, 7), 32599, 27]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁰⁴, 4686, F₂, 7, 27) (dual of [(4686, 7), 32598, 28]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰⁵, 4686, F₂, 7, 27) (dual of [(4686, 7), 32597, 28]-NRT-code)	[i]
4	Linear OOA(2²⁰⁶, 4686, F₂, 7, 27) (dual of [(4686, 7), 32596, 28]-NRT-code)	[i]