MinT - Information on Result #2448937

Information on Result #2448937

Linear OOA(7⁷⁰, 49, F₇, 2, 40) (dual of [(49, 2), 28, 41]-NRT-code), using strength reduction based on linear OOA(7⁷⁰, 49, F₇, 2, 41) (dual of [(49, 2), 28, 42]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7⁵, 7, F₇, 2, 5) (dual of [(7, 2), 9, 6]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(2;9,7) [i]
2. 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]
3. 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]
4. linear OOA(7¹⁰, 7, F₇, 2, 10) (dual of [(7, 2), 4, 11]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(2;4,7) [i]
5. 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]
6. 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]
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(7⁷², 50, F₇, 2, 40) (dual of [(50, 2), 28, 41]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(7⁷¹, 49, F₇, 2, 40) (dual of [(49, 2), 27, 41]-NRT-code)	[i]		OOA Duplication