Problem in understanding Blakley's Secret Sharing Scheme

I need to implement Blakley's Secret Sharing Scheme. I have read below mentioned two research papers but still unable to understand how to implement it.

1. Safeguarding cryptographic keys

2. Two Matrices for Blakley’s Secret Sharing Scheme

The following is the steps I have been able to understand.



a. We chose positive integers "z", "a" and "b".

b. We chose a large "p"

c. A (a+b+2) x (b+2) matrix M is created satisfying the following conditions-

• Random entry in each row is set to 1.


• Another random entry in 1st row is set to k, chosen from F (field modulo p)


• All other entries are filled with random values from F.
  
  After this some equation need to be formed and then solved for share.
  

I am unable to understand how shares are calculated and how can they be verified. Kindly help me understand the remaining process.

Thank you in advance.