MinT - Information on Result #2642328

Information on Result #2642328

Linear OOA(7⁸⁶, 35, F₇, 3, 58) (dual of [(35, 3), 19, 59]-NRT-code), using strength reduction based on linear OOA(7⁸⁶, 35, F₇, 3, 59) (dual of [(35, 3), 19, 60]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. 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(7¹⁴, 7, F₇, 3, 14) (dual of [(7, 3), 7, 15]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;7,7) [i]
3. linear OOA(7¹⁹, 7, F₇, 3, 19) (dual of [(7, 3), 2, 20]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;2,7) [i]
4. linear OOA(7²¹, 7, F₇, 3, 21) (dual of [(7, 3), 0, 22]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
5. linear OOA(7²¹, 7, F₇, 3, 21) (dual of [(7, 3), 0, 22]-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		Method
1	Linear OOA(7⁸⁵, 34, F₇, 3, 57) (dual of [(34, 3), 17, 58]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(7⁸⁴, 34, F₇, 3, 56) (dual of [(34, 3), 18, 57]-NRT-code)	[i]
3	Linear OOA(7⁸³, 34, F₇, 3, 55) (dual of [(34, 3), 19, 56]-NRT-code)	[i]
4	Linear OOA(7⁸², 33, F₇, 3, 54) (dual of [(33, 3), 17, 55]-NRT-code)	[i]
5	Linear OOA(7⁸¹, 33, F₇, 3, 53) (dual of [(33, 3), 18, 54]-NRT-code)	[i]
6	Linear OOA(7⁸⁰, 33, F₇, 3, 52) (dual of [(33, 3), 19, 53]-NRT-code)	[i]