MinT - Information on Result #630716

Information on Result #630716

Linear OA(3⁶², 84, F₃, 29) (dual of [84, 22, 30]-code), using concatenation of two codes based on

linear OA(9¹⁷, 28, F₉, 14) (dual of [28, 11, 15]-code), using
- extended algebraic-geometric code AG_e(F,13P) [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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3⁶², 84, F₃, 28) (dual of [84, 22, 29]-code)	[i]		Strength Reduction
2	Linear OA(3⁶³, 85, F₃, 29) (dual of [85, 22, 30]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(3⁶¹, 83, F₃, 28) (dual of [83, 22, 29]-code)	[i]		Truncation
4	Linear OOA(3⁶², 42, F₃, 2, 29) (dual of [(42, 2), 22, 30]-NRT-code)	[i]		OOA Folding
5	Linear OOA(3⁶², 28, F₃, 3, 29) (dual of [(28, 3), 22, 30]-NRT-code)	[i]		OOA Folding