MinT - Information on Result #1297737

Information on Result #1297737

Linear OA(2²⁴⁹, 393, F₂, 66) (dual of [393, 144, 67]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(2²⁴⁸, 391, F₂, 66) (dual of [391, 143, 67]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(2²⁴⁴, 384, F₂, 67) (dual of [384, 140, 68]-code), using
    - concatenation of two codes [i] based on
      1. linear OA(32³⁶, 64, F₃₂, 33) (dual of [64, 28, 34]-code), using
        extended algebraic-geometric code AG_e(F,30P) [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
        a function field by SÃ©mirat [i]
      2. linear OA(2¹, 6, F₂, 1) (dual of [6, 5, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OA(2²⁴⁴, 387, F₂, 64) (dual of [387, 143, 65]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2²⁴⁴Â > V_b^sâˆ’1(kâˆ’1)Â = 26 582889 062260 337326 040139 982427 472904 534025 371389 547780 098797 925201 260308 [i]
  3. linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
linear OA(2²⁴⁸, 392, F₂, 65) (dual of [392, 144, 66]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2²⁴⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 329 860683 003135 392546 552516 937810 123101 254278 957946 389007 774609 348223 597346 [i]
linear OA(2⁰, 1, F₂, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2⁰, s, F₂, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [i]

Mode: 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 OA(2²⁵⁰, 394, F₂, 67) (dual of [394, 144, 68]-code)	[i]		Adding a Parity Check Bit