Were there implicit laws not referenced in the Acts 15 letter to gentile believers? In Acts 29 the Jewish Christian Elders in Jerusalem sent a letter to the gentile believers throughout the world, instructing them to be at peace, and stating that they were not required to follow Jewish tradition.


  For it has seemed good to the Holy Spirit and to us to lay on you no greater burden than these requirements:  that you abstain from what has been sacrificed to idols, and from blood, and from what has been strangled, and from sexual immorality. If you keep yourselves from these, you will do well. Farewell. Acts 15:28-29 ESV


This is obviously in response to the circumcision party, and it's fairly obvious that they're saying circumcision and the dietary laws were not required of gentiles, but it doesn't seem to saying anything about the laws we still consider core (murder, covetousness, stealing, etc).  

Was there some implicit set of laws that was not referenced, but would be understood by both parties to be in effect?
The laws that were stated here are laws about ones self not pertaining to love. We know from the new testament that the thing we are commanded to do is to love. 


  John 13:34 NIV
  
  A new commandment I give to you, that you love one another; as I have
  loved you, that you also love one another.


We also know that it is love which fulfills the law.


  Romans 13:10
  
  Love does no harm to a neighbor; therefore love is the fulfillment of
  the law.


In the letter that you're quoting in your question, the Elders are telling people about the laws that are not under the law of love. Thus you don't have to worry about those laws. For the law is fulfilled in love.


  Matthew 22:37-40 (NIV)
  
  37 Jesus replied: “‘Love the Lord your God with all your heart and
  with all your soul and with all your mind.’ 38 This is the first
  and greatest commandment. 39 And the second is like it: ‘Love your
  neighbor as yourself.’ 40 All the Law and the Prophets hang on
  these two commandments.”


The laws that you're asking about: stealing, murder, covetousness we are still commanded to follow because those are under the law of love.