MinT - Information on Result #2447306

Information on Result #2447306

Linear OOA(5⁹⁵, 50, F₅, 2, 77) (dual of [(50, 2), 5, 78]-NRT-code), using strength reduction based on linear OOA(5⁹⁵, 50, F₅, 2, 79) (dual of [(50, 2), 5, 80]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(5¹⁶, 10, F₅, 2, 15) (dual of [(10, 2), 4, 16]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₅ with g(F) = 1 and N(F) ≥ 10, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(5¹⁹, 10, F₅, 2, 19) (dual of [(10, 2), 1, 20]-NRT-code), using
  - dual of repetition NRT-code with length 10 [i]
3. linear OOA(5²⁰, 10, F₅, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
4. linear OOA(5²⁰, 10, F₅, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code) (see above)
5. linear OOA(5²⁰, 10, F₅, 2, 20) (dual of [(10, 2), 0, 21]-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(5⁹⁴, 49, F₅, 2, 76) (dual of [(49, 2), 4, 77]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(5⁹³, 49, F₅, 2, 75) (dual of [(49, 2), 5, 76]-NRT-code)	[i]
3	Linear OOA(5⁹¹, 48, F₅, 2, 73) (dual of [(48, 2), 5, 74]-NRT-code)	[i]
4	Linear OOA(5⁸⁹, 47, F₅, 2, 71) (dual of [(47, 2), 5, 72]-NRT-code)	[i]
5	Linear OOA(5⁸⁷, 46, F₅, 2, 69) (dual of [(46, 2), 5, 70]-NRT-code)	[i]