MinT - Information on Result #1151744

Information on Result #1151744

Linear OOA(2²⁴⁶, 599190, F₂, 7, 23) (dual of [(599190, 7), 4194084, 24]-NRT-code), using OOA 7-folding based on linear OA(2²⁴⁶, 4194330, F₂, 23) (dual of [4194330, 4194084, 24]-code), using

2 times code embedding in larger space [i] based on linear OA(2²⁴⁴, 4194328, F₂, 23) (dual of [4194328, 4194084, 24]-code), using
- constructionÂ X4 applied to C_e(22) âŠ‚ C_e(20) [i] based on
  1. linear OA(2²⁴³, 4194304, F₂, 23) (dual of [4194304, 4194061, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 2²²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  2. linear OA(2²²¹, 4194304, F₂, 21) (dual of [4194304, 4194083, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 2²²âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
  3. linear OA(2²³, 24, F₂, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
    - dual of repetition code with length 24 [i]
  4. linear OA(2¹, 24, F₂, 1) (dual of [24, 23, 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(2²⁴⁷, 599190, F₂, 7, 23) (dual of [(599190, 7), 4194083, 24]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁴⁸, 599190, F₂, 7, 23) (dual of [(599190, 7), 4194082, 24]-NRT-code)	[i]
3	Linear OOA(2²⁴⁹, 599190, F₂, 7, 23) (dual of [(599190, 7), 4194081, 24]-NRT-code)	[i]
4	Linear OOA(2²⁴⁵, 599189, F₂, 7, 22) (dual of [(599189, 7), 4194078, 23]-NRT-code)	[i]	Truncation for OOAs