MinT - Information on Result #1680203

Information on Result #1680203

Linear OOA(2¹¹⁰, 65541, F₂, 7, 12) (dual of [(65541, 7), 458677, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹¹⁰, 65541, F₂, 4, 12) (dual of [(65541, 4), 262054, 13]-NRT-code), using

OOA 4-folding [i] based on linear OA(2¹¹⁰, 262164, F₂, 12) (dual of [262164, 262054, 13]-code), using
- strength reduction [i] based on linear OA(2¹¹⁰, 262164, F₂, 13) (dual of [262164, 262054, 14]-code), using
  - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [i] based on
    1. linear OA(2¹⁰⁹, 262144, F₂, 13) (dual of [262144, 262035, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(2⁹¹, 262144, F₂, 11) (dual of [262144, 262053, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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, 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		This result only	Method
1	Linear OOA(2¹¹¹, 65541, F₂, 7, 12) (dual of [(65541, 7), 458676, 13]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹¹², 65541, F₂, 7, 12) (dual of [(65541, 7), 458675, 13]-NRT-code)	[i]
3	Linear OOA(2¹¹³, 65541, F₂, 7, 12) (dual of [(65541, 7), 458674, 13]-NRT-code)	[i]