MinT - Information on Result #2242145

Information on Result #2242145

Linear OA(4¹⁵⁷, 259, F₄, 62) (dual of [259, 102, 63]-code), using 1 times truncation based on linear OA(4¹⁵⁸, 260, F₄, 63) (dual of [260, 102, 64]-code), using

concatenation of two codes [i] based on
1. linear OA(64³¹, 65, F₆₄, 31) (dual of [65, 34, 32]-code or 65-arc in PG(30,64)), using
  - extended Reedâ€“Solomon code RS_e(34,64) [i]
  - the expurgated narrow-sense BCH-code C(I) with length 65Â | 64²âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
2. linear OA(4¹, 4, F₄, 1) (dual of [4, 3, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 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		Method
1	Linear OA(4¹⁵⁹, 261, F₄, 62) (dual of [261, 102, 63]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(4¹⁶⁰, 262, F₄, 62) (dual of [262, 102, 63]-code)	[i]
3	Linear OA(4¹⁶¹, 263, F₄, 62) (dual of [263, 102, 63]-code)	[i]
4	Linear OOA(4¹⁵⁷, 129, F₄, 2, 62) (dual of [(129, 2), 101, 63]-NRT-code)	[i]	OOA Folding
5	Linear OOA(4¹⁵⁷, 86, F₄, 3, 62) (dual of [(86, 3), 101, 63]-NRT-code)	[i]	OOA Folding