MinT - Information on Result #2437954

Information on Result #2437954

Linear OOA(3²⁴⁵, 136, F₃, 2, 148) (dual of [(136, 2), 27, 149]-NRT-code), using strength reduction based on linear OOA(3²⁴⁵, 136, F₃, 2, 149) (dual of [(136, 2), 27, 150]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(27²⁵, 34, F₂₇, 24) (dual of [34, 9, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(27²⁵, 38, F₂₇, 24) (dual of [38, 13, 25]-code), using
    - extended algebraic-geometric code AG_e(F,13P) [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]
2. linear OOA(3⁵, 4, F₃, 2, 5) (dual of [(4, 2), 3, 6]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;3,3) [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(3²⁴⁷, 137, F₃, 2, 148) (dual of [(137, 2), 27, 149]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3²⁴⁶, 136, F₃, 2, 148) (dual of [(136, 2), 26, 149]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3²⁴⁴, 135, F₃, 2, 147) (dual of [(135, 2), 26, 148]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(3²⁴³, 135, F₃, 2, 146) (dual of [(135, 2), 27, 147]-NRT-code)	[i]
5	Linear OOA(3²⁴², 134, F₃, 2, 145) (dual of [(134, 2), 26, 146]-NRT-code)	[i]
6	Linear OOA(3²⁴¹, 134, F₃, 2, 144) (dual of [(134, 2), 27, 145]-NRT-code)	[i]
7	Linear OOA(3²⁴⁰, 133, F₃, 2, 143) (dual of [(133, 2), 26, 144]-NRT-code)	[i]
8	Linear OOA(3²³⁹, 133, F₃, 2, 142) (dual of [(133, 2), 27, 143]-NRT-code)	[i]
9	Linear OOA(3²³⁸, 132, F₃, 2, 141) (dual of [(132, 2), 26, 142]-NRT-code)	[i]
10	Linear OOA(3²⁴⁵, 68, F₃, 4, 148) (dual of [(68, 4), 27, 149]-NRT-code)	[i]	OOA Folding