MinT - Information on Result #909754

Information on Result #909754

Linear OOA(4⁸⁷, 46, F₄, 2, 68) (dual of [(46, 2), 5, 69]-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(4⁵⁹, 32, F₄, 2, 47) (dual of [(32, 2), 5, 48]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4¹², 8, F₄, 2, 11) (dual of [(8, 2), 4, 12]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4¹², 9, F₄, 2, 11) (dual of [(9, 2), 6, 12]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,6P) [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(4¹⁵, 8, F₄, 2, 15) (dual of [(8, 2), 1, 16]-NRT-code), using
    - dual of repetition NRT-code with length 8 [i]
  3. linear OOA(4¹⁶, 8, F₄, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4¹⁶, 8, F₄, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4⁸⁷, 46, F₄, 2, 67) (dual of [(46, 2), 5, 68]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4⁸⁷, 46, F₄, 2, 66) (dual of [(46, 2), 5, 67]-NRT-code)	[i]		Strength Reduction for OOAs