MinT - Information on Result #1649146

Information on Result #1649146

Linear OOA(3²¹², 154318, F₃, 5, 26) (dual of [(154318, 5), 771378, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹², 154318, F₃, 3, 26) (dual of [(154318, 3), 462742, 27]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²¹², 177161, F₃, 3, 26) (dual of [(177161, 3), 531271, 27]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3²¹¹, 177161, F₃, 3, 26) (dual of [(177161, 3), 531272, 27]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3²¹¹, 531483, F₃, 26) (dual of [531483, 531272, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(21) [i] based on
      1. linear OA(3²⁰⁵, 531441, F₃, 26) (dual of [531441, 531236, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      2. linear OA(3¹⁶⁹, 531441, F₃, 22) (dual of [531441, 531272, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      3. linear OA(3⁶, 42, F₃, 3) (dual of [42, 36, 4]-code or 42-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(3²¹², 51439, F₃, 35, 26) (dual of [(51439, 35), 1800153, 27]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row