MinT - Information on Result #2448925

Information on Result #2448925

Linear OOA(7⁶⁹, 42, F₇, 2, 46) (dual of [(42, 2), 15, 47]-NRT-code), using strength reduction based on linear OOA(7⁶⁹, 42, F₇, 2, 47) (dual of [(42, 2), 15, 48]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7⁶, 6, F₇, 2, 6) (dual of [(6, 2), 6, 7]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7⁶, 7, F₇, 2, 6) (dual of [(7, 2), 8, 7]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;8,7) [i]
2. linear OOA(7⁷, 6, F₇, 2, 7) (dual of [(6, 2), 5, 8]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7⁷, 7, F₇, 2, 7) (dual of [(7, 2), 7, 8]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;7,7) [i]
3. linear OOA(7⁹, 6, F₇, 2, 9) (dual of [(6, 2), 3, 10]-NRT-code), using
  - discarding factors / shortening the dual code based on 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]
4. linear OOA(7¹¹, 6, F₇, 2, 11) (dual of [(6, 2), 1, 12]-NRT-code), using
  - dual of repetition NRT-code with length 6 [i]
5. linear OOA(7¹², 6, F₇, 2, 12) (dual of [(6, 2), 0, 13]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
6. linear OOA(7¹², 6, F₇, 2, 12) (dual of [(6, 2), 0, 13]-NRT-code) (see above)
7. linear OOA(7¹², 6, F₇, 2, 12) (dual of [(6, 2), 0, 13]-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(7⁷¹, 43, F₇, 2, 46) (dual of [(43, 2), 15, 47]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(7⁶⁸, 41, F₇, 2, 45) (dual of [(41, 2), 14, 46]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(7⁶⁷, 41, F₇, 2, 44) (dual of [(41, 2), 15, 45]-NRT-code)	[i]	Truncation for OOAs