MinT - Information on Result #2419942

Information on Result #2419942

Linear OOA(2¹³⁵, 96, F₂, 2, 52) (dual of [(96, 2), 57, 53]-NRT-code), using strength reduction based on linear OOA(2¹³⁵, 96, F₂, 2, 53) (dual of [(96, 2), 57, 54]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8²⁹, 24, F₈, 2, 26) (dual of [(24, 2), 19, 27]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,21P) [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		Method
1	Linear OOA(2¹³⁷, 97, F₂, 2, 52) (dual of [(97, 2), 57, 53]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹³⁶, 96, F₂, 2, 52) (dual of [(96, 2), 56, 53]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹³⁵, 48, F₂, 4, 52) (dual of [(48, 4), 57, 53]-NRT-code)	[i]	OOA Folding