MinT - Information on Result #2248120

Information on Result #2248120

Linear OA(7⁵⁷, 83, F₇, 30) (dual of [83, 26, 31]-code), using 1 times truncation based on linear OA(7⁵⁸, 84, F₇, 31) (dual of [84, 26, 32]-code), using

concatenation of two codes [i] based on
1. linear OA(49¹⁵, 28, F₄₉, 15) (dual of [28, 13, 16]-code or 28-arc in PG(14,49)), using
  - discarding factors / shortening the dual code based on linear OA(49¹⁵, 49, F₄₉, 15) (dual of [49, 34, 16]-code or 49-arc in PG(14,49)), using
    - Reedâ€“Solomon code RS(34,49) [i]
2. linear OA(7¹, 3, F₇, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(7¹, s, F₇, 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7⁵⁷, 41, F₇, 2, 30) (dual of [(41, 2), 25, 31]-NRT-code)	[i]		OOA Folding
2	Linear OOA(7⁵⁷, 27, F₇, 3, 30) (dual of [(27, 3), 24, 31]-NRT-code)	[i]		OOA Folding