lower bound: | 32 |
upper bound: | 34 |
Construction of a linear code [78,11,32] over GF(2): [1]: [10, 3, 8] Linear Code over GF(2^3) Extended BCHCode over GF(8) with parameters 9 7 2 [2]: [10, 5, 4] Linear Code over GF(2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 1, 1, 1, 0 ] [ 0, 1, 0, 0, 0, 1, 0, 1, 1, 0 ] [ 0, 0, 1, 0, 0, 1, 1, 0, 1, 0 ] [ 0, 0, 0, 1, 0, 1, 1, 1, 0, 0 ] [ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ] [3]: [8, 4, 4] Quasicyclic of degree 2 Linear Code over GF(2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 1, 1, 1, 0 ] [ 0, 1, 0, 0, 0, 1, 1, 1 ] [ 0, 0, 1, 0, 1, 0, 1, 1 ] [ 0, 0, 0, 1, 1, 1, 0, 1 ] [4]: [8, 1, 8] Cyclic Linear Code over GF(2) RepetitionCode of length 8 [5]: [80, 14, 32] Linear Code over GF(2) ZinovievCode using inner codes: [4] [3], outer codes: [2] [1] [6]: [78, 13, 32] Linear Code over GF(2) Shortening of [5] at { 33, 73 } [7]: [78, 11, 32] Linear Code over GF(2) Subcode of [6] last modified: 2001-01-30
Lb(78,11) = 32 is found by taking a subcode of: Lb(78,13) = 32 To Ub(78,11) = 34 follows by a one-step Griesmer bound from: Ub(43,10) = 17 follows by a one-step Griesmer bound from: Ub(25,9) = 8 is found by considering shortening to: Ub(24,8) = 8 otherwise adding a parity check bit would contradict: Ub(25,8) = 9 YH1
YH1: Øyvind Ytrehus & Tor Helleseth, There is no binary [25,8,10] code, IEEE Trans. Inform. Theory 36 (May 1990) 695-696.
Notes
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