MinT - Information on Result #1750059

Information on Result #1750059

Digital (88, 98, 174770)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁹⁸, 174770, F₂, 3, 10) (dual of [(174770, 3), 524212, 11]-NRT-code), using

OOA 3-folding [i] based on linear OA(2⁹⁸, 524310, F₂, 10) (dual of [524310, 524212, 11]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2⁹⁶, 524308, F₂, 10) (dual of [524308, 524212, 11]-code), using
  - 1 times truncation [i] based on linear OA(2⁹⁷, 524309, F₂, 11) (dual of [524309, 524212, 12]-code), using
    - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
      1. linear OA(2⁹⁶, 524288, F₂, 11) (dual of [524288, 524192, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      2. linear OA(2⁷⁷, 524288, F₂, 9) (dual of [524288, 524211, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      3. linear OA(2²⁰, 21, F₂, 19) (dual of [21, 1, 20]-code), using
        strength reduction [i] based on linear OA(2²⁰, 21, F₂, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
        dual of repetition code with length 21 [i]
      4. linear OA(2¹, 21, F₂, 1) (dual of [21, 20, 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 (89, 99, 174770)-net over F₂	[i]		Net Duplication