MinT - Information on Result #909731

Information on Result #909731

Linear OOA(4¹⁴³, 74, F₄, 2, 109) (dual of [(74, 2), 5, 110]-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(4¹²⁵, 65, F₄, 2, 96) (dual of [(65, 2), 5, 97]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4¹³, 9, F₄, 2, 12) (dual of [(9, 2), 5, 13]-NRT-code) (see above)
  2. linear OOA(4¹⁰⁷, 56, F₄, 2, 83) (dual of [(56, 2), 5, 84]-NRT-code), using
    - 7 step truncation [i] based on linear OOA(4¹¹⁴, 60, F₄, 2, 90) (dual of [(60, 2), 6, 91]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OA(16¹², 15, F₁₆, 12) (dual of [15, 3, 13]-code or 15-arc in PG(11,16)), using
        discarding factors / shortening the dual code based on linear OA(16¹², 16, F₁₆, 12) (dual of [16, 4, 13]-code or 16-arc in PG(11,16)), using
        Reedâ€“Solomon code RS(4,16) [i]
        linear OOA(4⁶, 4, F₄, 2, 6) (dual of [(4, 2), 2, 7]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(2;2,4) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹⁴³, 74, F₄, 2, 108) (dual of [(74, 2), 5, 109]-NRT-code)	[i]		Strength Reduction for OOAs