MinT - Information on Result #1597356

Information on Result #1597356

Linear OOA(2²²⁴, 1318, F₂, 4, 37) (dual of [(1318, 4), 5048, 38]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²²⁴, 1318, F₂, 3, 37) (dual of [(1318, 3), 3730, 38]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²²⁴, 1376, F₂, 3, 37) (dual of [(1376, 3), 3904, 38]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2²²⁴, 4128, F₂, 37) (dual of [4128, 3904, 38]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(2²²³, 4127, F₂, 37) (dual of [4127, 3904, 38]-code), using
    - constructionÂ X applied to C([0,18]) âŠ‚ C([0,16]) [i] based on
      1. linear OA(2²¹⁷, 4097, F₂, 37) (dual of [4097, 3880, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
      2. linear OA(2¹⁹³, 4097, F₂, 33) (dual of [4097, 3904, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [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(2²²⁴, 659, F₂, 7, 37) (dual of [(659, 7), 4389, 38]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²²⁴, 659, F₂, 8, 37) (dual of [(659, 8), 5048, 38]-NRT-code)	[i]		OOA Folding