MinT - Information on Result #1609805

Information on Result #1609805

Linear OOA(3²¹⁴, 448629, F₃, 4, 24) (dual of [(448629, 4), 1794302, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹⁴, 448629, F₃, 3, 24) (dual of [(448629, 3), 1345673, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²¹⁴, 531451, F₃, 3, 24) (dual of [(531451, 3), 1594139, 25]-NRT-code), using
- 1 step truncation [i] based on linear OOA(3²¹⁵, 531452, F₃, 3, 25) (dual of [(531452, 3), 1594141, 26]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3²¹⁵, 1594356, F₃, 25) (dual of [1594356, 1594141, 26]-code), using
    - constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
      1. linear OA(3²⁰⁹, 1594324, F₃, 25) (dual of [1594324, 1594115, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      2. linear OA(3¹⁸³, 1594324, F₃, 21) (dual of [1594324, 1594141, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      3. linear OA(3⁶, 32, F₃, 3) (dual of [32, 26, 4]-code or 32-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(3²¹⁴, 149542, F₃, 28, 24) (dual of [(149542, 28), 4186962, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row