MinT - Information on Result #840110

Information on Result #840110

Linear OOA(5¹⁴⁷, 77, F₅, 2, 113) (dual of [(77, 2), 7, 114]-NRT-code), using OOA 2-folding based on linear OA(5¹⁴⁷, 154, F₅, 113) (dual of [154, 7, 114]-code), using

discarding factors / shortening the dual code based on linear OA(5¹⁴⁷, 155, F₅, 113) (dual of [155, 8, 114]-code), using
- 1 times truncation [i] 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 OOA(5¹⁴⁷, 77, F₅, 2, 112) (dual of [(77, 2), 7, 113]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(5¹⁴⁷, 77, F₅, 2, 111) (dual of [(77, 2), 7, 112]-NRT-code)	[i]
3	Linear OOA(5¹⁴⁷, 77, F₅, 2, 110) (dual of [(77, 2), 7, 111]-NRT-code)	[i]