MinT - Information on Result #1610153

Information on Result #1610153

Linear OOA(3²¹⁸, 20856, F₃, 4, 32) (dual of [(20856, 4), 83206, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹⁸, 20856, F₃, 2, 32) (dual of [(20856, 2), 41494, 33]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²¹⁸, 29543, F₃, 2, 32) (dual of [(29543, 2), 58868, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²¹⁸, 59086, F₃, 32) (dual of [59086, 58868, 33]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3²¹⁷, 59085, F₃, 32) (dual of [59085, 58868, 33]-code), using
    - constructionÂ X applied to C_e(31) âŠ‚ C_e(27) [i] based on
      1. linear OA(3²¹¹, 59049, F₃, 32) (dual of [59049, 58838, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
      2. linear OA(3¹⁸¹, 59049, F₃, 28) (dual of [59049, 58868, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      3. linear OA(3⁶, 36, F₃, 3) (dual of [36, 30, 4]-code or 36-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(3²¹⁸, 5213, F₃, 36, 32) (dual of [(5213, 36), 187450, 33]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row