MinT - Information on Result #1131607

Information on Result #1131607

Linear OOA(2²⁰⁵, 699059, F₂, 6, 18) (dual of [(699059, 6), 4194149, 19]-NRT-code), using OOA 6-folding based on linear OA(2²⁰⁵, 4194354, F₂, 18) (dual of [4194354, 4194149, 19]-code), using

1 times truncation [i] based on linear OA(2²⁰⁶, 4194355, F₂, 19) (dual of [4194355, 4194149, 20]-code), using
- constructionÂ X applied to C_e(18) âŠ‚ C_e(14) [i] based on
  1. linear OA(2¹⁹⁹, 4194304, F₂, 19) (dual of [4194304, 4194105, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 2²²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  2. linear OA(2¹⁵⁵, 4194304, F₂, 15) (dual of [4194304, 4194149, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 2²²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
  3. linear OA(2⁷, 51, F₂, 3) (dual of [51, 44, 4]-code or 51-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(2²⁰⁵, 699059, F₂, 7, 18) (dual of [(699059, 7), 4893208, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁰⁵, 699059, F₂, 8, 18) (dual of [(699059, 8), 5592267, 19]-NRT-code)	[i]
3	Digital (187, 205, 699059)-net over F₂	[i]