MinT - Information on Result #2642353

Information on Result #2642353

Linear OOA(7⁸⁸, 36, F₇, 3, 58) (dual of [(36, 3), 20, 59]-NRT-code), using strength reduction based on linear OOA(7⁸⁸, 36, F₇, 3, 59) (dual of [(36, 3), 20, 60]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7⁹, 6, F₇, 3, 9) (dual of [(6, 3), 9, 10]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7⁹, 7, F₇, 3, 9) (dual of [(7, 3), 12, 10]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;12,7) [i]
2. linear OOA(7¹¹, 6, F₇, 3, 11) (dual of [(6, 3), 7, 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]
3. linear OOA(7¹⁴, 6, F₇, 3, 14) (dual of [(6, 3), 4, 15]-NRT-code), using
  - discarding factors / shortening the dual code based on 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]
4. linear OOA(7¹⁸, 6, F₇, 3, 18) (dual of [(6, 3), 0, 19]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
5. linear OOA(7¹⁸, 6, F₇, 3, 18) (dual of [(6, 3), 0, 19]-NRT-code) (see above)
6. linear OOA(7¹⁸, 6, F₇, 3, 18) (dual of [(6, 3), 0, 19]-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(7⁸⁹, 36, F₇, 3, 58) (dual of [(36, 3), 19, 59]-NRT-code)	[i]		OOA Duplication