MinT - Information on Result #1651018

Information on Result #1651018

Linear OOA(3²³³, 9766, F₃, 5, 38) (dual of [(9766, 5), 48597, 39]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²³³, 9766, F₃, 2, 38) (dual of [(9766, 2), 19299, 39]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²³³, 9858, F₃, 2, 38) (dual of [(9858, 2), 19483, 39]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3²³², 9858, F₃, 2, 38) (dual of [(9858, 2), 19484, 39]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3²³², 19716, F₃, 38) (dual of [19716, 19484, 39]-code), using
    - constructionÂ X applied to C_e(37) âŠ‚ C_e(33) [i] based on
      1. linear OA(3²²⁶, 19683, F₃, 38) (dual of [19683, 19457, 39]-code), using an extension C_e(37) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,37], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
      2. linear OA(3¹⁹⁹, 19683, F₃, 34) (dual of [19683, 19484, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
      3. linear OA(3⁶, 33, F₃, 3) (dual of [33, 27, 4]-code or 33-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(3²³³, 2441, F₃, 45, 38) (dual of [(2441, 45), 109612, 39]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row