MinT - Information on Result #2486236

Information on Result #2486236

Linear OOA(3¹¹⁹, 29543, F₃, 2, 17) (dual of [(29543, 2), 58967, 18]-NRT-code), using 3¹ times duplication 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: Constructive and 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		Method
1	Linear OOA(3¹¹⁹, 29350, F₃, 3, 17) (dual of [(29350, 3), 87931, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹¹⁹, 29350, F₃, 4, 17) (dual of [(29350, 4), 117281, 18]-NRT-code)	[i]
3	Linear OOA(3¹¹⁹, 29350, F₃, 5, 17) (dual of [(29350, 5), 146631, 18]-NRT-code)	[i]
4	Digital (102, 119, 29350)-net over F₃	[i]