MinT - Information on Result #2233709

Information on Result #2233709

Linear OA(3¹⁸⁴, 271, F₃, 68) (dual of [271, 87, 69]-code), using 1 times truncation based on linear OA(3¹⁸⁵, 272, F₃, 69) (dual of [272, 87, 70]-code), using

concatenation of two codes [i] based on
1. linear OA(27³⁹, 68, F₂₇, 34) (dual of [68, 29, 35]-code), using
  - extended algebraic-geometric code AG_e(F,33P) [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]
2. linear OA(3¹, 4, F₃, 1) (dual of [4, 3, 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OA(3¹⁸⁶, 273, F₃, 68) (dual of [273, 87, 69]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(3¹⁸⁷, 274, F₃, 68) (dual of [274, 87, 69]-code)	[i]
3	Linear OA(3¹⁸⁸, 275, F₃, 68) (dual of [275, 87, 69]-code)	[i]
4	Linear OOA(3¹⁸⁴, 135, F₃, 2, 68) (dual of [(135, 2), 86, 69]-NRT-code)	[i]	OOA Folding
5	Linear OOA(3¹⁸⁴, 90, F₃, 3, 68) (dual of [(90, 3), 86, 69]-NRT-code)	[i]	OOA Folding