MinT - Information on Result #953055

Information on Result #953055

Linear OOA(3¹⁸³, 531445, F₃, 3, 21) (dual of [(531445, 3), 1594152, 22]-NRT-code), using OOA 3-folding based on linear OA(3¹⁸³, 1594335, F₃, 21) (dual of [1594335, 1594152, 22]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁸³, 1594336, F₃, 21) (dual of [1594336, 1594153, 22]-code), using
- 1 times truncation [i] based on linear OA(3¹⁸⁴, 1594337, F₃, 22) (dual of [1594337, 1594153, 23]-code), using
  - constructionÂ X applied to C_e(21) âŠ‚ C_e(19) [i] based on
    1. linear OA(3¹⁸³, 1594323, F₃, 22) (dual of [1594323, 1594140, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    2. linear OA(3¹⁷⁰, 1594323, F₃, 20) (dual of [1594323, 1594153, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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(3¹⁸³, 404362, F₃, 4, 21) (dual of [(404362, 4), 1617265, 22]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁸³, 404362, F₃, 5, 21) (dual of [(404362, 5), 2021627, 22]-NRT-code)	[i]
3	Digital (162, 183, 404362)-net over F₃	[i]