MinT - Information on Result #1027482

Information on Result #1027482

Linear OOA(4¹³⁷, 47, F₄, 3, 117) (dual of [(47, 3), 4, 118]-NRT-code), using juxtaposition based on

linear OOA(4⁸, 4, F₄, 3, 8) (dual of [(4, 3), 4, 9]-NRT-code), using
- Reedâ€“Solomon NRT-code RS(3;4,4) [i]
linear OOA(4¹²⁵, 43, F₄, 3, 108) (dual of [(43, 3), 4, 109]-NRT-code), using
- strength reduction [i] based on linear OOA(4¹²⁵, 43, F₄, 3, 109) (dual of [(43, 3), 4, 110]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(4³⁸, 14, F₄, 3, 35) (dual of [(14, 3), 4, 36]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,6P) [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(4⁸³, 29, F₄, 3, 73) (dual of [(29, 3), 4, 74]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(4³⁸, 14, F₄, 3, 35) (dual of [(14, 3), 4, 36]-NRT-code) (see above)
        linear OOA(4⁴¹, 15, F₄, 3, 37) (dual of [(15, 3), 4, 38]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹³⁷, 47, F₄, 3, 116) (dual of [(47, 3), 4, 117]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4¹³⁷, 47, F₄, 3, 115) (dual of [(47, 3), 4, 116]-NRT-code)	[i]		Strength Reduction for OOAs