MinT - Information on Result #1591367

Information on Result #1591367

Linear OOA(2¹³⁷, 2235, F₂, 4, 20) (dual of [(2235, 4), 8803, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹³⁷, 2235, F₂, 3, 20) (dual of [(2235, 3), 6568, 21]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹³⁷, 2741, F₂, 3, 20) (dual of [(2741, 3), 8086, 21]-NRT-code), using
- strength reduction [i] based on linear OOA(2¹³⁷, 2741, F₂, 3, 21) (dual of [(2741, 3), 8086, 22]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2¹³⁷, 8223, F₂, 21) (dual of [8223, 8086, 22]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹³⁷, 8225, F₂, 21) (dual of [8225, 8088, 22]-code), using
      - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
        linear OA(2¹³¹, 8193, F₂, 21) (dual of [8193, 8062, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
        linear OA(2¹⁰⁵, 8193, F₂, 17) (dual of [8193, 8088, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [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(2¹³⁷, 1117, F₂, 8, 20) (dual of [(1117, 8), 8799, 21]-NRT-code)	[i]		OOA Folding