MinT - Information on Result #2426843

Information on Result #2426843

Linear OOA(2²³⁰, 140, F₂, 2, 93) (dual of [(140, 2), 50, 94]-NRT-code), using strength reduction based on linear OOA(2²³⁰, 140, F₂, 2, 94) (dual of [(140, 2), 50, 95]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁸, 28, F₃₂, 18) (dual of [28, 10, 19]-code or 28-arc in PG(17,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁸, 32, F₃₂, 18) (dual of [32, 14, 19]-code or 32-arc in PG(17,32)), using
    - Reedâ€“Solomon code RS(14,32) [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(2²³², 141, F₂, 2, 93) (dual of [(141, 2), 50, 94]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²³¹, 140, F₂, 2, 93) (dual of [(140, 2), 49, 94]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²²⁹, 139, F₂, 2, 92) (dual of [(139, 2), 49, 93]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²²⁸, 139, F₂, 2, 91) (dual of [(139, 2), 50, 92]-NRT-code)	[i]
5	Linear OOA(2²²⁷, 138, F₂, 2, 90) (dual of [(138, 2), 49, 91]-NRT-code)	[i]
6	Linear OOA(2²³⁰, 70, F₂, 4, 93) (dual of [(70, 4), 50, 94]-NRT-code)	[i]	OOA Folding