MinT - Information on Result #2461564

Information on Result #2461564

Linear OOA(2²³³, 224, F₂, 2, 64) (dual of [(224, 2), 215, 65]-NRT-code), using 1 step truncation based on linear OOA(2²³⁴, 225, F₂, 2, 65) (dual of [(225, 2), 216, 66]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16³⁶, 45, F₁₆, 2, 32) (dual of [(45, 2), 54, 33]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,57P) [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]
2. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 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(2²³³, 112, F₂, 4, 64) (dual of [(112, 4), 215, 65]-NRT-code)	[i]	OOA Folding
2	Linear OOA(2²³³, 74, F₂, 5, 64) (dual of [(74, 5), 137, 65]-NRT-code)	[i]
3	Linear OOA(2²³³, 74, F₂, 6, 64) (dual of [(74, 6), 211, 65]-NRT-code)	[i]