MinT - Information on Result #1645511

Information on Result #1645511

Linear OOA(3¹⁶⁴, 424447, F₃, 5, 19) (dual of [(424447, 5), 2122071, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶⁴, 424447, F₃, 3, 19) (dual of [(424447, 3), 1273177, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁶⁴, 531452, F₃, 3, 19) (dual of [(531452, 3), 1594192, 20]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁶³, 531452, F₃, 3, 19) (dual of [(531452, 3), 1594193, 20]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁶³, 1594356, F₃, 19) (dual of [1594356, 1594193, 20]-code), using
    - constructionÂ X applied to C([0,9]) âŠ‚ C([0,7]) [i] based on
      1. linear OA(3¹⁵⁷, 1594324, F₃, 19) (dual of [1594324, 1594167, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      2. linear OA(3¹³¹, 1594324, F₃, 15) (dual of [1594324, 1594193, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (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(3¹⁶⁴, 212223, F₃, 25, 19) (dual of [(212223, 25), 5305411, 20]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row