MinT - Information on Result #1525007

Information on Result #1525007

Linear OOA(3¹⁶¹, 9349, F₃, 3, 26) (dual of [(9349, 3), 27886, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶¹, 9349, F₃, 2, 26) (dual of [(9349, 2), 18537, 27]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁶¹, 9858, F₃, 2, 26) (dual of [(9858, 2), 19555, 27]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁶⁰, 9858, F₃, 2, 26) (dual of [(9858, 2), 19556, 27]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁶⁰, 19716, F₃, 26) (dual of [19716, 19556, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(21) [i] based on
      1. linear OA(3¹⁵⁴, 19683, F₃, 26) (dual of [19683, 19529, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      2. linear OA(3¹²⁷, 19683, F₃, 22) (dual of [19683, 19556, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [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(3¹⁶¹, 4674, F₃, 5, 26) (dual of [(4674, 5), 23209, 27]-NRT-code)	[i]		OOA Folding