MinT - Information on Result #907994

Information on Result #907994

Linear OOA(4²¹⁴, 110, F₄, 2, 163) (dual of [(110, 2), 6, 164]-NRT-code), using repeating each code word 2 times based on linear OOA(4¹⁰⁴, 55, F₄, 2, 81) (dual of [(55, 2), 6, 82]-NRT-code), using

2 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(4²²⁶, 116, F₄, 2, 169) (dual of [(116, 2), 6, 170]-NRT-code)	[i]		Juxtaposition for OOAs