MinT - Information on Result #2448970

Information on Result #2448970

Linear OOA(7⁷³, 40, F₇, 2, 58) (dual of [(40, 2), 7, 59]-NRT-code), using strength reduction based on linear OOA(7⁷³, 40, F₇, 2, 59) (dual of [(40, 2), 7, 60]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. 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]
2. 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]
3. 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]
4. linear OOA(7¹⁶, 8, F₇, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code) (see above)
5. 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		Method
1	Linear OOA(7⁷², 39, F₇, 2, 57) (dual of [(39, 2), 6, 58]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(7⁷¹, 39, F₇, 2, 56) (dual of [(39, 2), 7, 57]-NRT-code)	[i]
3	Linear OOA(7⁷⁰, 38, F₇, 2, 55) (dual of [(38, 2), 6, 56]-NRT-code)	[i]
4	Linear OOA(7⁶⁹, 38, F₇, 2, 54) (dual of [(38, 2), 7, 55]-NRT-code)	[i]
5	Linear OOA(7⁶⁸, 37, F₇, 2, 53) (dual of [(37, 2), 6, 54]-NRT-code)	[i]
6	Linear OOA(7⁶⁷, 37, F₇, 2, 52) (dual of [(37, 2), 7, 53]-NRT-code)	[i]
7	Linear OOA(7⁶⁵, 36, F₇, 2, 50) (dual of [(36, 2), 7, 51]-NRT-code)	[i]