MinT - Information on Result #1752580

Information on Result #1752580

Digital (139, 158, 21849)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁵⁸, 21849, F₂, 6, 19) (dual of [(21849, 6), 130936, 20]-NRT-code), using

OOA 6-folding [i] based on linear OA(2¹⁵⁸, 131094, F₂, 19) (dual of [131094, 130936, 20]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2¹⁵⁶, 131092, F₂, 19) (dual of [131092, 130936, 20]-code), using
  - adding a parity check bit [i] based on linear OA(2¹⁵⁵, 131091, F₂, 18) (dual of [131091, 130936, 19]-code), using
    - constructionÂ X4 applied to C([0,18]) âŠ‚ C([1,16]) [i] based on
      1. linear OA(2¹⁵⁴, 131071, F₂, 19) (dual of [131071, 130917, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [0,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(2¹³⁶, 131071, F₂, 16) (dual of [131071, 130935, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      3. linear OA(2¹⁹, 20, F₂, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
        dual of repetition code with length 20 [i]
      4. linear OA(2¹, 20, F₂, 1) (dual of [20, 19, 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: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (140, 159, 21849)-net over F₂	[i]		Net Duplication