MinT - Information on Result #2468676

Information on Result #2468676

Linear OOA(4¹⁰⁵, 55, F₄, 2, 82) (dual of [(55, 2), 5, 83]-NRT-code), using 1 step truncation 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		Method
1	Linear OOA(4²¹⁵, 110, F₄, 2, 165) (dual of [(110, 2), 5, 166]-NRT-code)	[i]	Repeating Each Code Word for NRT-Codes
2	Linear OOA(4¹³³, 69, F₄, 2, 103) (dual of [(69, 2), 5, 104]-NRT-code)	[i]	Juxtaposition for OOAs
3	Linear OOA(4¹⁶⁹, 87, F₄, 2, 130) (dual of [(87, 2), 5, 131]-NRT-code)	[i]
4	Linear OOA(4¹⁷⁷, 91, F₄, 2, 136) (dual of [(91, 2), 5, 137]-NRT-code)	[i]
5	Linear OOA(4¹⁸⁵, 95, F₄, 2, 142) (dual of [(95, 2), 5, 143]-NRT-code)	[i]
6	Linear OOA(4²⁰¹, 103, F₄, 2, 154) (dual of [(103, 2), 5, 155]-NRT-code)	[i]
7	Linear OOA(4²⁰⁹, 107, F₄, 2, 160) (dual of [(107, 2), 5, 161]-NRT-code)	[i]