MinT - Information on Result #2919283

Information on Result #2919283

Linear OOA(2²²³, 699054, F₂, 6, 20) (dual of [(699054, 6), 4194101, 21]-NRT-code), using 1 step truncation based on linear OOA(2²²⁴, 699055, F₂, 6, 21) (dual of [(699055, 6), 4194106, 22]-NRT-code), using

OOA 6-folding [i] based on linear OA(2²²⁴, 4194330, F₂, 21) (dual of [4194330, 4194106, 22]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2²²², 4194328, F₂, 21) (dual of [4194328, 4194106, 22]-code), using
  - constructionÂ X4 applied to C_e(20) âŠ‚ C_e(18) [i] based on
    1. 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]
    2. 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]
    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(2²²³, 600175, F₂, 7, 20) (dual of [(600175, 7), 4201002, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²²³, 600175, F₂, 8, 20) (dual of [(600175, 8), 4801177, 21]-NRT-code)	[i]
3	Digital (203, 223, 600175)-net over F₂	[i]