MinT - Information on Result #2677007

Information on Result #2677007

Linear OOA(3¹⁵⁷, 1594328, F₃, 3, 17) (dual of [(1594328, 3), 4782827, 18]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁵⁶, 1594328, F₃, 3, 17) (dual of [(1594328, 3), 4782828, 18]-NRT-code), using

OOA 3-folding [i] based on linear OA(3¹⁵⁶, 4782984, F₃, 17) (dual of [4782984, 4782828, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3¹⁵⁵, 4782983, F₃, 17) (dual of [4782983, 4782828, 18]-code), using
  - constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
    1. linear OA(3¹⁵⁵, 4782969, F₃, 17) (dual of [4782969, 4782814, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    2. linear OA(3¹⁴¹, 4782969, F₃, 16) (dual of [4782969, 4782828, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    3. linear OA(3⁰, 14, F₃, 0) (dual of [14, 14, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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(3¹⁵⁷, 1271815, F₃, 4, 17) (dual of [(1271815, 4), 5087103, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁵⁷, 1271815, F₃, 5, 17) (dual of [(1271815, 5), 6358918, 18]-NRT-code)	[i]
3	Digital (140, 157, 1271815)-net over F₃	[i]