MinT - Information on Result #2671237

Information on Result #2671237

Linear OOA(2¹⁷⁷, 101, F₂, 3, 59) (dual of [(101, 3), 126, 60]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁷⁴, 100, F₂, 3, 59) (dual of [(100, 3), 126, 60]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8³³, 25, F₈, 3, 29) (dual of [(25, 3), 42, 30]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,45P) [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, 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		This result only	Method
1	Linear OOA(2¹⁷⁸, 101, F₂, 3, 59) (dual of [(101, 3), 125, 60]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹⁷⁹, 101, F₂, 3, 59) (dual of [(101, 3), 124, 60]-NRT-code)	[i]		OOA Duplication