MinT - Information on Result #2481895

Information on Result #2481895

Linear OOA(2¹⁵², 97, F₂, 2, 63) (dual of [(97, 2), 42, 64]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁵⁰, 96, F₂, 2, 63) (dual of [(96, 2), 42, 64]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8³⁴, 24, F₈, 2, 31) (dual of [(24, 2), 14, 32]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,16P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
    - the Klein quartic over F₈ [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(2¹⁵³, 97, F₂, 2, 63) (dual of [(97, 2), 41, 64]-NRT-code)	[i]		OOA Duplication