MinT - Information on Result #2233706

Information on Result #2233706

Linear OA(3¹⁹⁸, 255, F₃, 82) (dual of [255, 57, 83]-code), using 1 times truncation based on linear OA(3¹⁹⁹, 256, F₃, 83) (dual of [256, 57, 84]-code), using

concatenation of two codes [i] based on
1. linear OA(27⁴⁵, 64, F₂₇, 41) (dual of [64, 19, 42]-code), using
  - extended algebraic-geometric code AG_e(F,22P) [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, 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(3²⁰⁰, 257, F₃, 82) (dual of [257, 57, 83]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(3²⁰¹, 258, F₃, 82) (dual of [258, 57, 83]-code)	[i]
3	Linear OA(3²⁰², 259, F₃, 82) (dual of [259, 57, 83]-code)	[i]
4	Linear OOA(3¹⁹⁸, 127, F₃, 2, 82) (dual of [(127, 2), 56, 83]-NRT-code)	[i]	OOA Folding
5	Linear OOA(3¹⁹⁸, 85, F₃, 3, 82) (dual of [(85, 3), 57, 83]-NRT-code)	[i]	OOA Folding