MinT - Information on Result #909628

Information on Result #909628

Linear OOA(4⁸⁶, 46, F₄, 2, 64) (dual of [(46, 2), 6, 65]-NRT-code), using juxtaposition based on

linear OOA(4¹⁴, 10, F₄, 2, 12) (dual of [(10, 2), 6, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₄ with g(F) = 2 and N(F) ≥ 10, using
  - an explicitly constructive algebraic function field [i]
linear OOA(4⁶⁶, 36, F₄, 2, 51) (dual of [(36, 2), 6, 52]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. 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]
  2. linear OOA(4¹⁷, 9, F₄, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
    - dual of repetition NRT-code with length 9 [i]
  3. linear OOA(4¹⁸, 9, F₄, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4¹⁸, 9, F₄, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4⁸⁶, 46, F₄, 2, 63) (dual of [(46, 2), 6, 64]-NRT-code)	[i]		Strength Reduction for OOAs