MinT - Information on Result #2765959

Information on Result #2765959

Linear OOA(2²²⁵, 60, F₂, 4, 145) (dual of [(60, 4), 15, 146]-NRT-code), using strength reduction based on linear OOA(2²²⁵, 60, F₂, 4, 149) (dual of [(60, 4), 15, 150]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32⁹, 12, F₃₂, 9) (dual of [12, 3, 10]-code or 12-arc in PG(8,32)), using
  - discarding factors / shortening the dual code based on linear OA(32⁹, 32, F₃₂, 9) (dual of [32, 23, 10]-code or 32-arc in PG(8,32)), using
    - Reedâ€“Solomon code RS(23,32) [i]
2. linear OOA(2¹⁵, 5, F₂, 4, 14) (dual of [(5, 4), 5, 15]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;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(2²²⁴, 59, F₂, 4, 144) (dual of [(59, 4), 12, 145]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²²³, 59, F₂, 4, 143) (dual of [(59, 4), 13, 144]-NRT-code)	[i]
3	Linear OOA(2²²², 59, F₂, 4, 142) (dual of [(59, 4), 14, 143]-NRT-code)	[i]
4	Linear OOA(2²²¹, 59, F₂, 4, 141) (dual of [(59, 4), 15, 142]-NRT-code)	[i]
5	Linear OOA(2²¹⁸, 58, F₂, 4, 138) (dual of [(58, 4), 14, 139]-NRT-code)	[i]
6	Linear OOA(2²¹⁷, 58, F₂, 4, 137) (dual of [(58, 4), 15, 138]-NRT-code)	[i]
7	Linear OOA(2²²⁵, 30, F₂, 8, 145) (dual of [(30, 8), 15, 146]-NRT-code)	[i]	OOA Folding