MinT - Information on Result #1595621

Information on Result #1595621

Linear OOA(2²⁰⁴, 2204, F₂, 4, 30) (dual of [(2204, 4), 8612, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁰⁴, 2204, F₂, 3, 30) (dual of [(2204, 3), 6408, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁰⁴, 2742, F₂, 3, 30) (dual of [(2742, 3), 8022, 31]-NRT-code), using
- strength reduction [i] based on linear OOA(2²⁰⁴, 2742, F₂, 3, 31) (dual of [(2742, 3), 8022, 32]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2²⁰⁴, 8226, F₂, 31) (dual of [8226, 8022, 32]-code), using
    - 2 times code embedding in larger space [i] based on linear OA(2²⁰², 8224, F₂, 31) (dual of [8224, 8022, 32]-code), using
      - constructionÂ X applied to C_e(30) âŠ‚ C_e(26) [i] based on
        linear OA(2¹⁹⁶, 8192, F₂, 31) (dual of [8192, 7996, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
        linear OA(2¹⁷⁰, 8192, F₂, 27) (dual of [8192, 8022, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
        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(2²⁰⁴, 1102, F₂, 8, 30) (dual of [(1102, 8), 8612, 31]-NRT-code)	[i]		OOA Folding