- galois.ReedSolomon.detect(codeword: ArrayLike) bool | ndarray
Detects if errors are present in the codeword \(\mathbf{c}\).
Shortened codes
For the shortened \([n-s,\ k-s,\ d]\) code (only applicable for systematic codes), pass \(n-s\) symbols into
detect()
.- Parameters¶
- Returns¶
A boolean scalar or \(N\)-length array indicating if errors were detected in the corresponding codeword.
Examples¶
Encode a single message using the \(\textrm{RS}(15, 9)\) code.
In [1]: rs = galois.ReedSolomon(15, 9) In [2]: GF = rs.field In [3]: m = GF.Random(rs.k); m Out[3]: GF([13, 14, 9, 10, 15, 4, 11, 6, 12], order=2^4) In [4]: c = rs.encode(m); c Out[4]: GF([13, 14, 9, 10, 15, 4, 11, 6, 12, 9, 11, 4, 8, 11, 1], order=2^4)
Detect no errors in the valid codeword.
In [5]: rs.detect(c) Out[5]: False
Detect \(d_{min}-1\) errors in the codeword.
In [6]: rs.d Out[6]: 7 In [7]: e = GF.Random(rs.d - 1, low=1); e Out[7]: GF([ 8, 2, 14, 6, 4, 2], order=2^4) In [8]: c[0:rs.d - 1] += e; c Out[8]: GF([ 5, 12, 7, 12, 11, 6, 11, 6, 12, 9, 11, 4, 8, 11, 1], order=2^4) In [9]: rs.detect(c) Out[9]: True
Encode a single message using the shortened \(\textrm{RS}(11, 5)\) code.
In [10]: rs = galois.ReedSolomon(15, 9) In [11]: GF = rs.field In [12]: m = GF.Random(rs.k - 4); m Out[12]: GF([ 6, 10, 7, 11, 9], order=2^4) In [13]: c = rs.encode(m); c Out[13]: GF([ 6, 10, 7, 11, 9, 9, 14, 9, 4, 2, 15], order=2^4)
Detect no errors in the valid codeword.
In [14]: rs.detect(c) Out[14]: False
Detect \(d_{min}-1\) errors in the codeword.
In [15]: rs.d Out[15]: 7 In [16]: e = GF.Random(rs.d - 1, low=1); e Out[16]: GF([15, 3, 12, 13, 5, 4], order=2^4) In [17]: c[0:rs.d - 1] += e; c Out[17]: GF([ 9, 9, 11, 6, 12, 13, 14, 9, 4, 2, 15], order=2^4) In [18]: rs.detect(c) Out[18]: True
Encode a matrix of three messages using the \(\textrm{RS}(15, 9)\) code.
In [19]: rs = galois.ReedSolomon(15, 9) In [20]: GF = rs.field In [21]: m = GF.Random((3, rs.k)); m Out[21]: GF([[13, 14, 11, 15, 2, 13, 0, 6, 11], [15, 15, 7, 2, 6, 6, 1, 1, 6], [ 8, 14, 7, 3, 7, 3, 12, 10, 13]], order=2^4) In [22]: c = rs.encode(m); c Out[22]: GF([[13, 14, 11, 15, 2, 13, 0, 6, 11, 15, 0, 11, 5, 9, 1], [15, 15, 7, 2, 6, 6, 1, 1, 6, 15, 10, 8, 13, 10, 6], [ 8, 14, 7, 3, 7, 3, 12, 10, 13, 15, 13, 5, 12, 14, 3]], order=2^4)
Detect no errors in the valid codewords.
In [23]: rs.detect(c) Out[23]: array([False, False, False])
Detect one, two, and \(d_{min}-1\) errors in the codewords.
In [24]: rs.d Out[24]: 7 In [25]: c[0, 0:1] += GF.Random(1, low=1) In [26]: c[1, 0:2] += GF.Random(2, low=1) In [27]: c[2, 0:rs.d - 1] += GF.Random(rs.d - 1, low=1) In [28]: c Out[28]: GF([[ 4, 14, 11, 15, 2, 13, 0, 6, 11, 15, 0, 11, 5, 9, 1], [11, 3, 7, 2, 6, 6, 1, 1, 6, 15, 10, 8, 13, 10, 6], [14, 6, 6, 9, 4, 11, 12, 10, 13, 15, 13, 5, 12, 14, 3]], order=2^4) In [29]: rs.detect(c) Out[29]: array([ True, True, True])
Encode a matrix of three messages using the shortened \(\textrm{RS}(11, 5)\) code.
In [30]: rs = galois.ReedSolomon(15, 9) In [31]: GF = rs.field In [32]: m = GF.Random((3, rs.k - 4)); m Out[32]: GF([[12, 3, 0, 3, 15], [ 9, 3, 1, 13, 6], [ 1, 15, 11, 2, 14]], order=2^4) In [33]: c = rs.encode(m); c Out[33]: GF([[12, 3, 0, 3, 15, 1, 9, 15, 2, 4, 6], [ 9, 3, 1, 13, 6, 3, 12, 10, 7, 12, 12], [ 1, 15, 11, 2, 14, 1, 6, 12, 3, 6, 13]], order=2^4)
Detect no errors in the valid codewords.
In [34]: rs.detect(c) Out[34]: array([False, False, False])
Detect one, two, and \(d_{min}-1\) errors in the codewords.
In [35]: rs.d Out[35]: 7 In [36]: c[0, 0:1] += GF.Random(1, low=1) In [37]: c[1, 0:2] += GF.Random(2, low=1) In [38]: c[2, 0:rs.d - 1] += GF.Random(rs.d - 1, low=1) In [39]: c Out[39]: GF([[ 5, 3, 0, 3, 15, 1, 9, 15, 2, 4, 6], [ 2, 9, 1, 13, 6, 3, 12, 10, 7, 12, 12], [12, 3, 1, 15, 11, 5, 6, 12, 3, 6, 13]], order=2^4) In [40]: rs.detect(c) Out[40]: array([ True, True, True])