MinT - Information on Result #2676888

Information on Result #2676888

Linear OOA(3¹³⁴, 531446, F₃, 3, 16) (dual of [(531446, 3), 1594204, 17]-NRT-code), using 3¹ times duplication based on linear OOA(3¹³³, 531446, F₃, 3, 16) (dual of [(531446, 3), 1594205, 17]-NRT-code), using

OOA 3-folding [i] based on linear OA(3¹³³, 1594338, F₃, 16) (dual of [1594338, 1594205, 17]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3¹³², 1594337, F₃, 16) (dual of [1594337, 1594205, 17]-code), using
  - constructionÂ X applied to C_e(15) âŠ‚ C_e(13) [i] based on
    1. linear OA(3¹³¹, 1594323, F₃, 16) (dual of [1594323, 1594192, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    2. linear OA(3¹¹⁸, 1594323, F₃, 14) (dual of [1594323, 1594205, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    3. linear OA(3¹, 14, F₃, 1) (dual of [14, 13, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(3¹³⁴, 427458, F₃, 4, 16) (dual of [(427458, 4), 1709698, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹³⁴, 427458, F₃, 5, 16) (dual of [(427458, 5), 2137156, 17]-NRT-code)	[i]
3	Digital (118, 134, 427458)-net over F₃	[i]