MinT - Information on Result #2449381

Information on Result #2449381

Linear OOA(7¹⁰⁴, 56, F₇, 2, 82) (dual of [(56, 2), 8, 83]-NRT-code), using strength reduction based on linear OOA(7¹⁰⁴, 56, F₇, 2, 83) (dual of [(56, 2), 8, 84]-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(7¹³, 8, F₇, 2, 13) (dual of [(8, 2), 3, 14]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;3,7) [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)
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		Method
1	Linear OOA(7¹⁰⁶, 57, F₇, 2, 82) (dual of [(57, 2), 8, 83]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(7¹⁰⁸, 58, F₇, 2, 82) (dual of [(58, 2), 8, 83]-NRT-code)	[i]
3	Linear OOA(7¹¹⁰, 59, F₇, 2, 82) (dual of [(59, 2), 8, 83]-NRT-code)	[i]
4	Linear OOA(7¹⁰², 55, F₇, 2, 80) (dual of [(55, 2), 8, 81]-NRT-code)	[i]	Truncation for OOAs
5	Linear OOA(7¹⁰⁰, 54, F₇, 2, 78) (dual of [(54, 2), 8, 79]-NRT-code)	[i]
6	Linear OOA(7⁹⁸, 53, F₇, 2, 76) (dual of [(53, 2), 8, 77]-NRT-code)	[i]
7	Linear OOA(7⁹⁰, 49, F₇, 2, 68) (dual of [(49, 2), 8, 69]-NRT-code)	[i]