MinT - Information on Result #2449104

Information on Result #2449104

Linear OOA(7⁸⁴, 49, F₇, 2, 58) (dual of [(49, 2), 14, 59]-NRT-code), using strength reduction based on linear OOA(7⁸⁴, 49, F₇, 2, 59) (dual of [(49, 2), 14, 60]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7⁸, 7, F₇, 2, 8) (dual of [(7, 2), 6, 9]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(2;6,7) [i]
2. linear OOA(7⁹, 7, F₇, 2, 9) (dual of [(7, 2), 5, 10]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(2;5,7) [i]
3. linear OOA(7¹¹, 7, F₇, 2, 11) (dual of [(7, 2), 3, 12]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(2;3,7) [i]
4. linear OOA(7¹⁴, 7, F₇, 2, 14) (dual of [(7, 2), 0, 15]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
5. linear OOA(7¹⁴, 7, F₇, 2, 14) (dual of [(7, 2), 0, 15]-NRT-code) (see above)
6. linear OOA(7¹⁴, 7, F₇, 2, 14) (dual of [(7, 2), 0, 15]-NRT-code) (see above)
7. linear OOA(7¹⁴, 7, F₇, 2, 14) (dual of [(7, 2), 0, 15]-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(7⁸⁵, 49, F₇, 2, 58) (dual of [(49, 2), 13, 59]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(7⁸³, 48, F₇, 2, 57) (dual of [(48, 2), 13, 58]-NRT-code)	[i]		Truncation for OOAs