MinT - Information on Result #634343

Information on Result #634343

Linear OA(4¹⁴⁹, 195, F₄, 73) (dual of [195, 46, 74]-code), using concatenation of two codes based on

linear OA(16⁴², 65, F₁₆, 36) (dual of [65, 23, 37]-code), using
- extended algebraic-geometric code AG_e(F,28P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
  - the Hermitian function field over F₁₆ [i]
linear OA(4¹, 3, F₄, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 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(4¹⁴⁹, 195, F₄, 72) (dual of [195, 46, 73]-code)	[i]		Strength Reduction
2	Linear OA(4¹⁵⁰, 196, F₄, 73) (dual of [196, 46, 74]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹⁴⁸, 194, F₄, 72) (dual of [194, 46, 73]-code)	[i]		Truncation
4	Linear OOA(4¹⁴⁹, 97, F₄, 2, 73) (dual of [(97, 2), 45, 74]-NRT-code)	[i]		OOA Folding
5	Linear OOA(4¹⁴⁹, 65, F₄, 3, 73) (dual of [(65, 3), 46, 74]-NRT-code)	[i]		OOA Folding