MinT - Information on Result #909771

Information on Result #909771

Linear OOA(4¹⁸³, 94, F₄, 2, 140) (dual of [(94, 2), 5, 141]-NRT-code), using juxtaposition based on

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]
linear OOA(4¹⁵⁵, 80, F₄, 2, 119) (dual of [(80, 2), 5, 120]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4³⁶, 20, F₄, 2, 29) (dual of [(20, 2), 4, 30]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4³⁶, 21, F₄, 2, 29) (dual of [(21, 2), 6, 30]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,12P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
        an explicitly constructive algebraic function field [i]
  2. linear OOA(4³⁹, 20, F₄, 2, 39) (dual of [(20, 2), 1, 40]-NRT-code), using
    - dual of repetition NRT-code with length 20 [i]
  3. linear OOA(4⁴⁰, 20, F₄, 2, 40) (dual of [(20, 2), 0, 41]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4⁴⁰, 20, F₄, 2, 40) (dual of [(20, 2), 0, 41]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹⁸³, 94, F₄, 2, 139) (dual of [(94, 2), 5, 140]-NRT-code)	[i]		Strength Reduction for OOAs