MinT - Information on Result #1131324

Information on Result #1131324

Linear OOA(2¹⁷⁷, 699054, F₂, 6, 16) (dual of [(699054, 6), 4194147, 17]-NRT-code), using OOA 6-folding based on linear OA(2¹⁷⁷, 4194324, F₂, 16) (dual of [4194324, 4194147, 17]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁷⁷, 4194327, F₂, 16) (dual of [4194327, 4194150, 17]-code), using
- 1 times truncation [i] based on linear OA(2¹⁷⁸, 4194328, F₂, 17) (dual of [4194328, 4194150, 18]-code), using
  - constructionÂ X4 applied to C_e(16) âŠ‚ C_e(14) [i] based on
    1. linear OA(2¹⁷⁷, 4194304, F₂, 17) (dual of [4194304, 4194127, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 2²²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(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(2¹⁷⁷, 699054, F₂, 7, 16) (dual of [(699054, 7), 4893201, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁷⁷, 699054, F₂, 8, 16) (dual of [(699054, 8), 5592255, 17]-NRT-code)	[i]
3	Digital (161, 177, 699054)-net over F₂	[i]