MinT - Information on Result #1590566

Information on Result #1590566

Linear OOA(2¹¹⁷, 1225, F₂, 4, 19) (dual of [(1225, 4), 4783, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹¹⁷, 1225, F₂, 3, 19) (dual of [(1225, 3), 3558, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹¹⁷, 1376, F₂, 3, 19) (dual of [(1376, 3), 4011, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2¹¹⁷, 4128, F₂, 19) (dual of [4128, 4011, 20]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(2¹¹⁵, 4126, F₂, 19) (dual of [4126, 4011, 20]-code), using
    - constructionÂ X applied to C_e(18) âŠ‚ C_e(14) [i] based on
      1. linear OA(2¹⁰⁹, 4096, F₂, 19) (dual of [4096, 3987, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      2. linear OA(2⁸⁵, 4096, F₂, 15) (dual of [4096, 4011, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
      3. linear OA(2⁶, 30, F₂, 3) (dual of [30, 24, 4]-code or 30-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(2¹¹⁷, 612, F₂, 7, 19) (dual of [(612, 7), 4167, 20]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹¹⁷, 612, F₂, 8, 19) (dual of [(612, 8), 4779, 20]-NRT-code)	[i]		OOA Folding