MinT - Information on Result #2438118

Information on Result #2438118

Linear OOA(3²⁴⁷, 140, F₃, 2, 142) (dual of [(140, 2), 33, 143]-NRT-code), using strength reduction based on linear OOA(3²⁴⁷, 140, F₃, 2, 143) (dual of [(140, 2), 33, 144]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(27²⁴, 35, F₂₇, 23) (dual of [35, 11, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(27²⁴, 38, F₂₇, 23) (dual of [38, 14, 24]-code), using
    - extended algebraic-geometric code AG_e(F,14P) [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(3²⁴⁹, 141, F₃, 2, 142) (dual of [(141, 2), 33, 143]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3²⁴⁸, 140, F₃, 2, 142) (dual of [(140, 2), 32, 143]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3²⁴⁶, 139, F₃, 2, 141) (dual of [(139, 2), 32, 142]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(3²⁴⁵, 139, F₃, 2, 140) (dual of [(139, 2), 33, 141]-NRT-code)	[i]
5	Linear OOA(3²⁴⁴, 138, F₃, 2, 139) (dual of [(138, 2), 32, 140]-NRT-code)	[i]
6	Linear OOA(3²⁴³, 138, F₃, 2, 138) (dual of [(138, 2), 33, 139]-NRT-code)	[i]
7	Linear OOA(3²⁴¹, 137, F₃, 2, 136) (dual of [(137, 2), 33, 137]-NRT-code)	[i]
8	Linear OOA(3²⁴⁷, 70, F₃, 4, 142) (dual of [(70, 4), 33, 143]-NRT-code)	[i]	OOA Folding