MinT - Information on Result #2486733

Information on Result #2486733

Linear OOA(3¹⁵⁹, 29543, F₃, 2, 23) (dual of [(29543, 2), 58927, 24]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁵⁸, 29543, F₃, 2, 23) (dual of [(29543, 2), 58928, 24]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹⁵⁸, 59086, F₃, 23) (dual of [59086, 58928, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3¹⁵⁷, 59085, F₃, 23) (dual of [59085, 58928, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
    1. linear OA(3¹⁵¹, 59049, F₃, 23) (dual of [59049, 58898, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. linear OA(3¹²¹, 59049, F₃, 19) (dual of [59049, 58928, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(3¹⁵⁹, 23085, F₃, 3, 23) (dual of [(23085, 3), 69096, 24]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁵⁹, 23085, F₃, 4, 23) (dual of [(23085, 4), 92181, 24]-NRT-code)	[i]
3	Linear OOA(3¹⁵⁹, 23085, F₃, 5, 23) (dual of [(23085, 5), 115266, 24]-NRT-code)	[i]
4	Digital (136, 159, 23085)-net over F₃	[i]