MinT - Information on Result #1751081

Information on Result #1751081

Digital (115, 127, 524293)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹²⁷, 524293, F₂, 4, 12) (dual of [(524293, 4), 2097045, 13]-NRT-code), using

OOA 4-folding [i] based on linear OA(2¹²⁷, 2097172, F₂, 12) (dual of [2097172, 2097045, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹²⁷, 2097174, F₂, 12) (dual of [2097174, 2097047, 13]-code), using
  - 1 times truncation [i] based on linear OA(2¹²⁸, 2097175, F₂, 13) (dual of [2097175, 2097047, 14]-code), using
    - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [i] based on
      1. linear OA(2¹²⁷, 2097152, F₂, 13) (dual of [2097152, 2097025, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(2¹⁰⁶, 2097152, F₂, 11) (dual of [2097152, 2097046, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 2²¹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(2²², 23, F₂, 21) (dual of [23, 1, 22]-code), using
        strength reduction [i] based on linear OA(2²², 23, F₂, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
        dual of repetition code with length 23 [i]
      4. linear OA(2¹, 23, F₂, 1) (dual of [23, 22, 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 (116, 128, 524293)-net over F₂	[i]		Net Duplication