MinT - Information on Result #1522628

Information on Result #1522628

Linear OOA(3¹¹⁸, 27134, F₃, 3, 17) (dual of [(27134, 3), 81284, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹¹⁸, 27134, F₃, 2, 17) (dual of [(27134, 2), 54150, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹¹⁸, 29543, F₃, 2, 17) (dual of [(29543, 2), 58968, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹¹⁸, 59086, F₃, 17) (dual of [59086, 58968, 18]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3¹¹⁷, 59085, F₃, 17) (dual of [59085, 58968, 18]-code), using
    - constructionÂ X applied to C_e(16) âŠ‚ C_e(12) [i] based on
      1. linear OA(3¹¹¹, 59049, F₃, 17) (dual of [59049, 58938, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      2. linear OA(3⁸¹, 59049, F₃, 13) (dual of [59049, 58968, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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(3¹¹⁸, 13567, F₃, 5, 17) (dual of [(13567, 5), 67717, 18]-NRT-code)	[i]		OOA Folding