MinT - Information on Result #1590986

Information on Result #1590986

Linear OOA(2¹²⁸, 759, F₂, 4, 22) (dual of [(759, 4), 2908, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹²⁸, 759, F₂, 2, 22) (dual of [(759, 2), 1390, 23]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹²⁸, 1038, F₂, 2, 22) (dual of [(1038, 2), 1948, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹²⁸, 2076, F₂, 22) (dual of [2076, 1948, 23]-code), using
  - strength reduction [i] based on linear OA(2¹²⁸, 2076, F₂, 23) (dual of [2076, 1948, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
      1. linear OA(2¹²², 2048, F₂, 23) (dual of [2048, 1926, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(2¹⁰⁰, 2048, F₂, 19) (dual of [2048, 1948, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(2¹²⁸, 379, F₂, 7, 22) (dual of [(379, 7), 2525, 23]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹²⁸, 379, F₂, 8, 22) (dual of [(379, 8), 2904, 23]-NRT-code)	[i]		OOA Folding