MinT - Information on Result #2449176

Information on Result #2449176

Linear OOA(7⁸⁹, 49, F₇, 2, 68) (dual of [(49, 2), 9, 69]-NRT-code), using strength reduction based on linear OOA(7⁸⁹, 49, F₇, 2, 69) (dual of [(49, 2), 9, 70]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. 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]
2. 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]
3. linear OOA(7¹³, 7, F₇, 2, 13) (dual of [(7, 2), 1, 14]-NRT-code), using
  - dual of repetition NRT-code with length 7 [i]
  - Reedâ€“Solomon NRT-code RS(2;1,7) [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		Method
1	Linear OOA(7⁹¹, 50, F₇, 2, 68) (dual of [(50, 2), 9, 69]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(7⁸⁷, 48, F₇, 2, 66) (dual of [(48, 2), 9, 67]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(7⁸⁵, 47, F₇, 2, 64) (dual of [(47, 2), 9, 65]-NRT-code)	[i]
4	Linear OOA(7⁸³, 46, F₇, 2, 62) (dual of [(46, 2), 9, 63]-NRT-code)	[i]
5	Linear OOA(7⁸², 45, F₇, 2, 61) (dual of [(45, 2), 8, 62]-NRT-code)	[i]
6	Linear OOA(7⁸¹, 45, F₇, 2, 60) (dual of [(45, 2), 9, 61]-NRT-code)	[i]
7	Linear OOA(7⁷⁹, 44, F₇, 2, 58) (dual of [(44, 2), 9, 59]-NRT-code)	[i]
8	Linear OOA(7⁷⁷, 43, F₇, 2, 56) (dual of [(43, 2), 9, 57]-NRT-code)	[i]
9	Linear OOA(7⁷⁵, 42, F₇, 2, 54) (dual of [(42, 2), 9, 55]-NRT-code)	[i]