MinT - Information on Result #1131951

Information on Result #1131951

Linear OOA(2¹⁸³, 43694, F₂, 6, 21) (dual of [(43694, 6), 261981, 22]-NRT-code), using OOA 6-folding based on linear OA(2¹⁸³, 262164, F₂, 21) (dual of [262164, 261981, 22]-code), using

1 times code embedding in larger space [i] based on linear OA(2¹⁸², 262163, F₂, 21) (dual of [262163, 261981, 22]-code), using
- constructionÂ X applied to C_e(20) âŠ‚ C_e(18) [i] based on
  1. linear OA(2¹⁸¹, 262144, F₂, 21) (dual of [262144, 261963, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
  2. linear OA(2¹⁶³, 262144, F₂, 19) (dual of [262144, 261981, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  3. linear OA(2¹, 19, F₂, 1) (dual of [19, 18, 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(2¹⁸⁴, 43694, F₂, 6, 21) (dual of [(43694, 6), 261980, 22]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁸⁵, 43694, F₂, 6, 21) (dual of [(43694, 6), 261979, 22]-NRT-code)	[i]
3	Linear OOA(2¹⁸⁶, 43694, F₂, 6, 21) (dual of [(43694, 6), 261978, 22]-NRT-code)	[i]
4	Linear OOA(2¹⁸³, 38647, F₂, 7, 21) (dual of [(38647, 7), 270346, 22]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Linear OOA(2¹⁸³, 38647, F₂, 8, 21) (dual of [(38647, 8), 308993, 22]-NRT-code)	[i]
6	Digital (162, 183, 38647)-net over F₂	[i]