MinT - Information on Result #2229786

Information on Result #2229786

Linear OA(3¹⁰³, 151, F₃, 42) (dual of [151, 48, 43]-code), using 1 times truncation based on linear OA(3¹⁰⁴, 152, F₃, 43) (dual of [152, 48, 44]-code), using

concatenation of two codes [i] based on
1. linear OA(27²², 38, F₂₇, 21) (dual of [38, 16, 22]-code), using
  - extended algebraic-geometric code AG_e(F,16P) [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, 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.

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		Method
1	Linear OA(3¹⁰⁵, 153, F₃, 42) (dual of [153, 48, 43]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(3¹⁰⁶, 154, F₃, 42) (dual of [154, 48, 43]-code)	[i]
3	Linear OA(3¹⁰⁷, 155, F₃, 42) (dual of [155, 48, 43]-code)	[i]
4	Linear OA(3¹⁰⁴, 153, F₃, 42) (dual of [153, 49, 43]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
5	Linear OOA(3¹⁰³, 75, F₃, 2, 42) (dual of [(75, 2), 47, 43]-NRT-code)	[i]	OOA Folding
6	Linear OOA(3¹⁰³, 50, F₃, 3, 42) (dual of [(50, 3), 47, 43]-NRT-code)	[i]	OOA Folding