MinT - Information on Result #1650569

Information on Result #1650569

Linear OOA(3²²⁸, 51662, F₃, 5, 31) (dual of [(51662, 5), 258082, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²⁸, 51662, F₃, 3, 31) (dual of [(51662, 3), 154758, 32]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²²⁸, 59059, F₃, 3, 31) (dual of [(59059, 3), 176949, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²²⁸, 177177, F₃, 31) (dual of [177177, 176949, 32]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3²²⁷, 177176, F₃, 31) (dual of [177176, 176949, 32]-code), using
    - constructionÂ X applied to C([0,15]) âŠ‚ C([0,13]) [i] based on
      1. linear OA(3²²¹, 177148, F₃, 31) (dual of [177148, 176927, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
      2. linear OA(3¹⁹⁹, 177148, F₃, 27) (dual of [177148, 176949, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
      3. linear OA(3⁶, 28, F₃, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,3)), using
        discarding factors / shortening the dual code based on linear OA(3⁶, 48, F₃, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
        large caps in PG(5,Â b) [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(3²²⁸, 17220, F₃, 35, 31) (dual of [(17220, 35), 602472, 32]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row