MinT - Information on Result #2618103

Information on Result #2618103

Linear OOA(2²³¹, 112, F₂, 3, 88) (dual of [(112, 3), 105, 89]-NRT-code), using strength reduction based on linear OOA(2²³¹, 112, F₂, 3, 89) (dual of [(112, 3), 105, 90]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8⁴⁹, 28, F₈, 3, 44) (dual of [(28, 3), 35, 45]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,39P) [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
    - a function field by SÃ©mirat [i]
2. linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 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 OOA(2²³⁴, 113, F₂, 3, 88) (dual of [(113, 3), 105, 89]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²³⁷, 114, F₂, 3, 88) (dual of [(114, 3), 105, 89]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2²³², 112, F₂, 3, 88) (dual of [(112, 3), 104, 89]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²³³, 112, F₂, 3, 88) (dual of [(112, 3), 103, 89]-NRT-code)	[i]	OOA Duplication
5	Linear OOA(2²³¹, 56, F₂, 5, 88) (dual of [(56, 5), 49, 89]-NRT-code)	[i]	OOA Folding
6	Linear OOA(2²³¹, 56, F₂, 6, 88) (dual of [(56, 6), 105, 89]-NRT-code)	[i]	OOA Folding