MinT - Information on Result #1593258

Information on Result #1593258

Linear OOA(2¹⁷², 820, F₂, 4, 30) (dual of [(820, 4), 3108, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁷², 820, F₂, 2, 30) (dual of [(820, 2), 1468, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁷², 1038, F₂, 2, 30) (dual of [(1038, 2), 1904, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹⁷², 2076, F₂, 30) (dual of [2076, 1904, 31]-code), using
  - strength reduction [i] based on linear OA(2¹⁷², 2076, F₂, 31) (dual of [2076, 1904, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(26) [i] based on
      1. linear OA(2¹⁶⁶, 2048, F₂, 31) (dual of [2048, 1882, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      2. linear OA(2¹⁴⁴, 2048, F₂, 27) (dual of [2048, 1904, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      3. linear OA(2⁶, 28, F₂, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
        discarding factors / shortening the dual code based on linear OA(2⁶, 32, F₂, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
        Reedâ€“Muller code RM(1,5) [i]
        caps in base bÂ =Â 2 [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(2¹⁷², 410, F₂, 7, 30) (dual of [(410, 7), 2698, 31]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁷², 410, F₂, 8, 30) (dual of [(410, 8), 3108, 31]-NRT-code)	[i]		OOA Folding