MinT - Information on Result #1704714

Information on Result #1704714

Linear OOA(2²³², 3766, F₂, 8, 32) (dual of [(3766, 8), 29896, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³², 3766, F₂, 4, 32) (dual of [(3766, 4), 14832, 33]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³², 4105, F₂, 4, 32) (dual of [(4105, 4), 16188, 33]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2²³², 16420, F₂, 32) (dual of [16420, 16188, 33]-code), using
  - strength reduction [i] based on linear OA(2²³², 16420, F₂, 33) (dual of [16420, 16188, 34]-code), using
    - constructionÂ X applied to C([0,16]) âŠ‚ C([0,14]) [i] based on
      1. linear OA(2²²⁵, 16385, F₂, 33) (dual of [16385, 16160, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 2²⁸âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
      2. linear OA(2¹⁹⁷, 16385, F₂, 29) (dual of [16385, 16188, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 2²⁸âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
      3. linear OA(2⁷, 35, F₂, 3) (dual of [35, 28, 4]-code or 35-cap in PG(6,2)), using
        discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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(2²³², 1882, F₂, 40, 32) (dual of [(1882, 40), 75048, 33]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row