MinT - Information on Result #2211283

Information on Result #2211283

Linear OA(5¹⁴⁸, 156, F₅, 112) (dual of [156, 8, 113]-code), using strength reduction based on linear OA(5¹⁴⁸, 156, F₅, 114) (dual of [156, 8, 115]-code), using

concatenation of two codes [i] based on
1. linear OA(25²², 26, F₂₅, 22) (dual of [26, 4, 23]-code or 26-arc in PG(21,25)), using
  - extended Reedâ€“Solomon code RS_e(4,25) [i]
  - algebraic-geometric code AG(F, Q+0P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using the rational function field F₂₅(x) [i]
  - algebraic-geometric code AG(F,1P) with degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
2. linear OA(5⁴, 6, F₅, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,5)), using
  - extended Reedâ€“Solomon code RS_e(2,5) [i]
  - Simplex code S(2,5) [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 OA(5¹⁴⁷, 155, F₅, 111) (dual of [155, 8, 112]-code)	[i]	Truncation
2	Linear OA(5¹⁴⁶, 154, F₅, 110) (dual of [154, 8, 111]-code)	[i]
3	Linear OA(5¹⁴⁵, 153, F₅, 109) (dual of [153, 8, 110]-code)	[i]
4	Linear OA(5¹⁴⁴, 152, F₅, 108) (dual of [152, 8, 109]-code)	[i]
5	Linear OA(5¹⁴³, 151, F₅, 107) (dual of [151, 8, 108]-code)	[i]
6	Linear OA(5¹⁴¹, 149, F₅, 105) (dual of [149, 8, 106]-code)	[i]
7	Linear OOA(5¹⁴⁸, 52, F₅, 3, 112) (dual of [(52, 3), 8, 113]-NRT-code)	[i]	OOA Folding