MinT - Information on Result #2449322

Information on Result #2449322

Linear OOA(7⁹⁹, 56, F₇, 2, 70) (dual of [(56, 2), 13, 71]-NRT-code), using strength reduction based on linear OOA(7⁹⁹, 56, F₇, 2, 71) (dual of [(56, 2), 13, 72]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7¹⁰, 8, F₇, 2, 10) (dual of [(8, 2), 6, 11]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;6,7) [i]
2. linear OOA(7¹¹, 8, F₇, 2, 11) (dual of [(8, 2), 5, 12]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;5,7) [i]
3. linear OOA(7¹⁴, 8, F₇, 2, 14) (dual of [(8, 2), 2, 15]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;2,7) [i]
4. linear OOA(7¹⁶, 8, F₇, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
5. linear OOA(7¹⁶, 8, F₇, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code) (see above)
6. linear OOA(7¹⁶, 8, F₇, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code) (see above)
7. linear OOA(7¹⁶, 8, F₇, 2, 16) (dual of [(8, 2), 0, 17]-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(7¹⁰¹, 57, F₇, 2, 70) (dual of [(57, 2), 13, 71]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(7¹⁰³, 58, F₇, 2, 70) (dual of [(58, 2), 13, 71]-NRT-code)	[i]		NRT-Code Embedding in Larger Space