MinT - Information on Result #1030455

Information on Result #1030455

Linear OOA(3²⁰⁹, 81, F₃, 3, 123) (dual of [(81, 3), 34, 124]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9⁶⁴, 27, F₉, 3, 61) (dual of [(27, 3), 17, 62]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9⁶⁴, 28, F₉, 3, 61) (dual of [(28, 3), 20, 62]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,22P) [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(3²⁰⁹, 81, F₃, 3, 122) (dual of [(81, 3), 34, 123]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²⁰⁹, 81, F₃, 3, 121) (dual of [(81, 3), 34, 122]-NRT-code)	[i]		Strength Reduction for OOAs