MinT - Information on Result #2435602

Information on Result #2435602

Linear OOA(3²⁰⁹, 148, F₃, 2, 88) (dual of [(148, 2), 87, 89]-NRT-code), using strength reduction based on linear OOA(3²⁰⁹, 148, F₃, 2, 89) (dual of [(148, 2), 87, 90]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(27⁴⁵, 37, F₂₇, 2, 44) (dual of [(37, 2), 29, 45]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(27⁴⁵, 38, F₂₇, 2, 44) (dual of [(38, 2), 31, 45]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,31P) [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 OA(3¹, 4, F₃, 1) (dual of [4, 3, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [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		This result only	Method
1	Linear OOA(3²⁰⁹, 74, F₃, 4, 88) (dual of [(74, 4), 87, 89]-NRT-code)	[i]		OOA Folding