MinT - Information on Result #1662451

Information on Result #1662451

Linear OOA(2⁹², 8396, F₂, 6, 12) (dual of [(8396, 6), 50284, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁹², 8396, F₂, 3, 12) (dual of [(8396, 3), 25096, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁹², 10928, F₂, 3, 12) (dual of [(10928, 3), 32692, 13]-NRT-code), using
- strength reduction [i] based on linear OOA(2⁹², 10928, F₂, 3, 13) (dual of [(10928, 3), 32692, 14]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2⁹², 32784, F₂, 13) (dual of [32784, 32692, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(10) [i] based on
      1. linear OA(2⁹¹, 32768, F₂, 13) (dual of [32768, 32677, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(2⁷⁶, 32768, F₂, 11) (dual of [32768, 32692, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(2¹, 16, F₂, 1) (dual of [16, 15, 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(2⁹², 8395, F₂, 7, 12) (dual of [(8395, 7), 58673, 13]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2⁹², 8395, F₂, 8, 12) (dual of [(8395, 8), 67068, 13]-NRT-code)	[i]
3	Linear OOA(2⁹², 8395, F₂, 18, 12) (dual of [(8395, 18), 151018, 13]-NRT-code)	[i]