MinT - Information on Result #2429379

Information on Result #2429379

Linear OOA(2²⁵⁶, 140, F₂, 2, 124) (dual of [(140, 2), 24, 125]-NRT-code), using strength reduction based on linear OOA(2²⁵⁶, 140, F₂, 2, 125) (dual of [(140, 2), 24, 126]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16²², 28, F₁₆, 20) (dual of [28, 6, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(16²², 33, F₁₆, 20) (dual of [33, 11, 21]-code), using
    - extended algebraic-geometric code AG_e(F,12P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]
2. linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [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(2²⁵⁸, 141, F₂, 2, 124) (dual of [(141, 2), 24, 125]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁶⁰, 142, F₂, 2, 124) (dual of [(142, 2), 24, 125]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2²⁵⁷, 140, F₂, 2, 124) (dual of [(140, 2), 23, 125]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²⁵⁵, 139, F₂, 2, 123) (dual of [(139, 2), 23, 124]-NRT-code)	[i]	Truncation for OOAs
5	Linear OOA(2²⁵⁴, 139, F₂, 2, 122) (dual of [(139, 2), 24, 123]-NRT-code)	[i]
6	Linear OOA(2²⁵³, 138, F₂, 2, 121) (dual of [(138, 2), 23, 122]-NRT-code)	[i]
7	Linear OOA(2²⁵², 138, F₂, 2, 120) (dual of [(138, 2), 24, 121]-NRT-code)	[i]
8	Linear OOA(2²⁵¹, 137, F₂, 2, 119) (dual of [(137, 2), 23, 120]-NRT-code)	[i]
9	Linear OOA(2²⁵⁰, 137, F₂, 2, 118) (dual of [(137, 2), 24, 119]-NRT-code)	[i]
10	Linear OOA(2²⁴⁹, 136, F₂, 2, 117) (dual of [(136, 2), 23, 118]-NRT-code)	[i]
11	Linear OOA(2²⁴⁸, 136, F₂, 2, 116) (dual of [(136, 2), 24, 117]-NRT-code)	[i]
12	Linear OOA(2²⁵⁶, 70, F₂, 4, 124) (dual of [(70, 4), 24, 125]-NRT-code)	[i]	OOA Folding