MinT - Information on Result #909568

Information on Result #909568

Linear OOA(4¹²³, 65, F₄, 2, 90) (dual of [(65, 2), 7, 91]-NRT-code), using juxtaposition based on

linear OOA(4¹¹, 9, F₄, 2, 10) (dual of [(9, 2), 7, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
  - the Hermitian function field over F₄ [i]
linear OOA(4¹⁰⁵, 56, F₄, 2, 79) (dual of [(56, 2), 7, 80]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4²², 14, F₄, 2, 19) (dual of [(14, 2), 6, 20]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,8P) [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, 26) (dual of [(14, 2), 1, 27]-NRT-code), using
    - strength reduction [i] based on 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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹²³, 65, F₄, 2, 89) (dual of [(65, 2), 7, 90]-NRT-code)	[i]		Strength Reduction for OOAs