MinT - Information on Result #909726

Information on Result #909726

Linear OOA(4⁹³, 49, F₄, 2, 72) (dual of [(49, 2), 5, 73]-NRT-code), using juxtaposition based on

linear OOA(4¹³, 9, F₄, 2, 12) (dual of [(9, 2), 5, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,5P) [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(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)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4⁹³, 49, F₄, 2, 71) (dual of [(49, 2), 5, 72]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4⁹³, 49, F₄, 2, 70) (dual of [(49, 2), 5, 71]-NRT-code)	[i]		Strength Reduction for OOAs