BURST ERROR CONTROL UEC / UEP CODES in .NET

Creation QR Code in .NET BURST ERROR CONTROL UEC / UEP CODES
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1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1
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H BEC
H SEC
Figure 10.9 Parity-check matrix of the (56, 50) B3 ECjSEC code with n0 4. Source: [NAM03]. 2003 IEICE Japan.
of the pattern and l w -bit burst errors at the end of the pattern, and in between there are no errors so that 0 < w < l. The following shows the parity-check matrix of the l-bit cyclic burst error correcting Fire code generated by g x xc 1 p x , where p x is a primitive polynomial with degree m ! l , c is an integer larger than or equal to 2l 1, and ne LCM 2m 1; c where LCM y; z is the least common multiple of y and z: 2 6 6 Ic Ic 6 6 6 e Hi 6 6j j j j 6 6 i i c 1 i c i 2c 1 a a 4a a j j j j j a
i ne c
3x 7 7 c Ic 7 7y 7x 7 : 10:6 j 7 7 i ne 1 7 m a 5 y j
In this case, a is a root of p x , and i is an arbitrary integer. From the preparation above, we have another type of Bl ECjSEC code shown in the following theorem. Theorem 10.12 The following parity-check matrix H shows a Bl ECjSEC code: H HBEC j HSEC , where e HBEC : c m n0 matrix deleting the last ne n0 columns in H0 shown in 10:6 with i 0; HSEC HA HB HG ;