MinT - Information on Result #909791

Information on Result #909791

Linear OOA(4¹⁸⁵, 95, F₄, 2, 142) (dual of [(95, 2), 5, 143]-NRT-code), using juxtaposition based on

linear OOA(4⁷⁵, 40, F₄, 2, 59) (dual of [(40, 2), 5, 60]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4¹⁶, 10, F₄, 2, 14) (dual of [(10, 2), 4, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₄ with g(F) = 2 and N(F) ≥ 10, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(4¹⁹, 10, F₄, 2, 19) (dual of [(10, 2), 1, 20]-NRT-code), using
    - dual of repetition NRT-code with length 10 [i]
  3. linear OOA(4²⁰, 10, F₄, 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(4²⁰, 10, F₄, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code) (see above)
linear OOA(4¹⁰⁵, 55, F₄, 2, 82) (dual of [(55, 2), 5, 83]-NRT-code), using
- 1 step truncation [i] based on linear OOA(4¹⁰⁶, 56, F₄, 2, 83) (dual of [(56, 2), 6, 84]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(4²³, 14, F₄, 2, 20) (dual of [(14, 2), 5, 21]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(4²⁷, 14, F₄, 2, 27) (dual of [(14, 2), 1, 28]-NRT-code), using
      - dual of repetition NRT-code with length 14 [i]
    3. linear OOA(4²⁸, 14, F₄, 2, 28) (dual of [(14, 2), 0, 29]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]
    4. linear OOA(4²⁸, 14, F₄, 2, 28) (dual of [(14, 2), 0, 29]-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(4¹⁸⁵, 95, F₄, 2, 141) (dual of [(95, 2), 5, 142]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4¹⁸⁵, 95, F₄, 2, 140) (dual of [(95, 2), 5, 141]-NRT-code)	[i]		Strength Reduction for OOAs