MinT - Information on Result #2767042

Information on Result #2767042

Linear OOA(2²⁴², 65, F₂, 4, 152) (dual of [(65, 4), 18, 153]-NRT-code), using strength reduction based on linear OOA(2²⁴², 65, F₂, 4, 153) (dual of [(65, 4), 18, 154]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(64¹⁰, 13, F₆₄, 10) (dual of [13, 3, 11]-code or 13-arc in PG(9,64)), using
  - discarding factors / shortening the dual code based on linear OA(64¹⁰, 64, F₆₄, 10) (dual of [64, 54, 11]-code or 64-arc in PG(9,64)), using
    - Reedâ€“Solomon code RS(54,64) [i]
2. linear OOA(2¹⁴, 5, F₂, 4, 13) (dual of [(5, 4), 6, 14]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,6P) [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(2²⁴³, 65, F₂, 4, 152) (dual of [(65, 4), 17, 153]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁴¹, 64, F₂, 4, 151) (dual of [(64, 4), 15, 152]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2²³⁹, 64, F₂, 4, 149) (dual of [(64, 4), 17, 150]-NRT-code)	[i]
4	Linear OOA(2²³⁸, 64, F₂, 4, 148) (dual of [(64, 4), 18, 149]-NRT-code)	[i]
5	Linear OOA(2²³⁵, 63, F₂, 4, 145) (dual of [(63, 4), 17, 146]-NRT-code)	[i]
6	Linear OOA(2²³⁴, 63, F₂, 4, 144) (dual of [(63, 4), 18, 145]-NRT-code)	[i]