MinT - Information on Result #2448422

Information on Result #2448422

Linear OOA(5¹⁴⁵, 75, F₅, 2, 118) (dual of [(75, 2), 5, 119]-NRT-code), using strength reduction based on linear OOA(5¹⁴⁵, 75, F₅, 2, 119) (dual of [(75, 2), 5, 120]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(5²⁶, 15, F₅, 2, 23) (dual of [(15, 2), 4, 24]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5²⁶, 16, F₅, 2, 23) (dual of [(16, 2), 6, 24]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₅ with g(F) = 3 and N(F) ≥ 16, using
      - an explicitly constructive algebraic function field [i]
2. linear OOA(5²⁹, 15, F₅, 2, 29) (dual of [(15, 2), 1, 30]-NRT-code), using
  - dual of repetition NRT-code with length 15 [i]
3. linear OOA(5³⁰, 15, F₅, 2, 30) (dual of [(15, 2), 0, 31]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
4. linear OOA(5³⁰, 15, F₅, 2, 30) (dual of [(15, 2), 0, 31]-NRT-code) (see above)
5. linear OOA(5³⁰, 15, F₅, 2, 30) (dual of [(15, 2), 0, 31]-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(5¹⁴³, 74, F₅, 2, 116) (dual of [(74, 2), 5, 117]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(5¹⁴¹, 73, F₅, 2, 114) (dual of [(73, 2), 5, 115]-NRT-code)	[i]
3	Linear OOA(5¹³⁹, 72, F₅, 2, 112) (dual of [(72, 2), 5, 113]-NRT-code)	[i]