MinT - Information on Result #2429257

Information on Result #2429257

Linear OOA(2²⁵⁵, 155, F₂, 2, 103) (dual of [(155, 2), 55, 104]-NRT-code), using strength reduction based on linear OOA(2²⁵⁵, 155, F₂, 2, 104) (dual of [(155, 2), 55, 105]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32²⁰, 31, F₃₂, 20) (dual of [31, 11, 21]-code or 31-arc in PG(19,32)), using
  - discarding factors / shortening the dual code based on linear OA(32²⁰, 32, F₃₂, 20) (dual of [32, 12, 21]-code or 32-arc in PG(19,32)), using
    - Reedâ€“Solomon code RS(12,32) [i]
2. linear OOA(2⁵, 5, F₂, 2, 4) (dual of [(5, 2), 5, 5]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,5P) [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(2²⁵⁷, 156, F₂, 2, 103) (dual of [(156, 2), 55, 104]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁵⁶, 155, F₂, 2, 103) (dual of [(155, 2), 54, 104]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁵⁴, 154, F₂, 2, 102) (dual of [(154, 2), 54, 103]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²⁵³, 154, F₂, 2, 101) (dual of [(154, 2), 55, 102]-NRT-code)	[i]
5	Linear OOA(2²⁵², 153, F₂, 2, 100) (dual of [(153, 2), 54, 101]-NRT-code)	[i]