MinT - Information on Result #1030197

Information on Result #1030197

Linear OOA(3¹⁵¹, 63, F₃, 3, 83) (dual of [(63, 3), 38, 84]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9⁴⁴, 21, F₉, 3, 41) (dual of [(21, 3), 19, 42]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9⁴⁴, 28, F₉, 3, 41) (dual of [(28, 3), 40, 42]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,42P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
    - the Hermitian function field over F₉ [i]
linear OA(3¹, 3, F₃, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁵¹, 63, F₃, 3, 82) (dual of [(63, 3), 38, 83]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁵¹, 63, F₃, 3, 81) (dual of [(63, 3), 38, 82]-NRT-code)	[i]		Strength Reduction for OOAs