MinT - Information on Result #1324230

Information on Result #1324230

Linear OA(4²⁴⁹, 4194388, F₄, 28) (dual of [4194388, 4194139, 29]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4²⁴⁶, 4194384, F₄, 28) (dual of [4194384, 4194138, 29]-code), using
- 1 times truncation [i] based on linear OA(4²⁴⁷, 4194385, F₄, 29) (dual of [4194385, 4194138, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(20) [i] based on
    1. linear OA(4²³², 4194304, F₄, 29) (dual of [4194304, 4194072, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    2. linear OA(4¹⁶⁶, 4194304, F₄, 21) (dual of [4194304, 4194138, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    3. linear OA(4¹⁵, 81, F₄, 7) (dual of [81, 66, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁵, 85, F₄, 7) (dual of [85, 70, 8]-code), using
        a code from Grasslâ€™s database [i]
linear OA(4²⁴⁶, 4194385, F₄, 25) (dual of [4194385, 4194139, 26]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4²⁴⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 400 141141 518491 306762 530221 699523 294735 621515 610733 253228 981622 997829 718688 484712 003611 207281 430459 058638 223371 102879 002690 788892 489413 156917 611644 [i]
linear OA(4², 3, F₄, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,4)), using
- dual of repetition code with length 3 [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 OOA(4²⁴⁹, 2097194, F₄, 2, 28) (dual of [(2097194, 2), 4194139, 29]-NRT-code)	[i]		OOA Folding