MinT - Information on Result #909635

Information on Result #909635

Linear OOA(4²³⁸, 122, F₄, 2, 180) (dual of [(122, 2), 6, 181]-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(4²¹⁸, 112, F₄, 2, 167) (dual of [(112, 2), 6, 168]-NRT-code), using
- repeating each code word 2 times [i] based on linear OOA(4¹⁰⁶, 56, F₄, 2, 83) (dual of [(56, 2), 6, 84]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. 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]
    2. 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(4²⁵⁸, 132, F₄, 2, 193) (dual of [(132, 2), 6, 194]-NRT-code)	[i]		Juxtaposition for OOAs
2	Linear OOA(4²⁶⁰, 133, F₄, 2, 194) (dual of [(133, 2), 6, 195]-NRT-code)	[i]		Juxtaposition for OOAs