MinT - Information on Result #2765741

Information on Result #2765741

Linear OOA(2²²², 60, F₂, 4, 138) (dual of [(60, 4), 18, 139]-NRT-code), using strength reduction based on linear OOA(2²²², 60, F₂, 4, 139) (dual of [(60, 4), 18, 140]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(64⁹, 12, F₆₄, 9) (dual of [12, 3, 10]-code or 12-arc in PG(8,64)), using
  - discarding factors / shortening the dual code based on linear OA(64⁹, 64, F₆₄, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), using
    - Reedâ€“Solomon code RS(55,64) [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(2²²⁶, 61, F₂, 4, 138) (dual of [(61, 4), 18, 139]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²²³, 60, F₂, 4, 138) (dual of [(60, 4), 17, 139]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²¹⁹, 59, F₂, 4, 135) (dual of [(59, 4), 17, 136]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²¹⁸, 59, F₂, 4, 134) (dual of [(59, 4), 18, 135]-NRT-code)	[i]
5	Linear OOA(2²¹⁵, 58, F₂, 4, 131) (dual of [(58, 4), 17, 132]-NRT-code)	[i]
6	Linear OOA(2²¹⁴, 58, F₂, 4, 130) (dual of [(58, 4), 18, 131]-NRT-code)	[i]
7	Linear OOA(2²¹¹, 57, F₂, 4, 127) (dual of [(57, 4), 17, 128]-NRT-code)	[i]
8	Linear OOA(2²¹⁰, 57, F₂, 4, 126) (dual of [(57, 4), 18, 127]-NRT-code)	[i]
9	Linear OOA(2²²², 30, F₂, 8, 138) (dual of [(30, 8), 18, 139]-NRT-code)	[i]	OOA Folding