MinT - Information on Result #2481845

Information on Result #2481845

Linear OOA(2¹³⁸, 82, F₂, 2, 62) (dual of [(82, 2), 26, 63]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹³⁶, 81, F₂, 2, 62) (dual of [(81, 2), 26, 63]-NRT-code), using

strength reduction [i] based on linear OOA(2¹³⁶, 81, F₂, 2, 63) (dual of [(81, 2), 26, 64]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(4⁴¹, 27, F₄, 2, 31) (dual of [(27, 2), 13, 32]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,22P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]
  2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 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(2¹³⁸, 41, F₂, 4, 62) (dual of [(41, 4), 26, 63]-NRT-code)	[i]		OOA Folding