MinT - Information on Result #2486474

Information on Result #2486474

Linear OOA(3¹³⁹, 29543, F₃, 2, 20) (dual of [(29543, 2), 58947, 21]-NRT-code), using 3¹ times duplication based on linear OOA(3¹³⁸, 29543, F₃, 2, 20) (dual of [(29543, 2), 58948, 21]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹³⁸, 59086, F₃, 20) (dual of [59086, 58948, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3¹³⁷, 59085, F₃, 20) (dual of [59085, 58948, 21]-code), using
  - constructionÂ X applied to C_e(19) âŠ‚ C_e(15) [i] based on
    1. linear OA(3¹³¹, 59049, F₃, 20) (dual of [59049, 58918, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    2. linear OA(3¹⁰¹, 59049, F₃, 16) (dual of [59049, 58948, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(3¹³⁹, 25100, F₃, 3, 20) (dual of [(25100, 3), 75161, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹³⁹, 25100, F₃, 4, 20) (dual of [(25100, 4), 100261, 21]-NRT-code)	[i]
3	Linear OOA(3¹³⁹, 25100, F₃, 5, 20) (dual of [(25100, 5), 125361, 21]-NRT-code)	[i]
4	Digital (119, 139, 25100)-net over F₃	[i]