MinT - Information on Result #2642565

Information on Result #2642565

Linear OOA(7⁹⁹, 35, F₇, 3, 82) (dual of [(35, 3), 6, 83]-NRT-code), using strength reduction based on linear OOA(7⁹⁹, 35, F₇, 3, 83) (dual of [(35, 3), 6, 84]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7¹¹, 5, F₇, 3, 11) (dual of [(5, 3), 4, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7¹¹, 7, F₇, 3, 11) (dual of [(7, 3), 10, 12]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;10,7) [i]
2. linear OOA(7¹³, 5, F₇, 3, 13) (dual of [(5, 3), 2, 14]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7¹³, 7, F₇, 3, 13) (dual of [(7, 3), 8, 14]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;8,7) [i]
3. linear OOA(7¹⁵, 5, F₇, 3, 15) (dual of [(5, 3), 0, 16]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
4. linear OOA(7¹⁵, 5, F₇, 3, 15) (dual of [(5, 3), 0, 16]-NRT-code) (see above)
5. linear OOA(7¹⁵, 5, F₇, 3, 15) (dual of [(5, 3), 0, 16]-NRT-code) (see above)
6. linear OOA(7¹⁵, 5, F₇, 3, 15) (dual of [(5, 3), 0, 16]-NRT-code) (see above)
7. linear OOA(7¹⁵, 5, F₇, 3, 15) (dual of [(5, 3), 0, 16]-NRT-code) (see above)

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		This result only	Method
1	Linear OOA(7⁹⁶, 34, F₇, 3, 79) (dual of [(34, 3), 6, 80]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(7⁹³, 33, F₇, 3, 76) (dual of [(33, 3), 6, 77]-NRT-code)	[i]		Truncation for OOAs