... of subspace a is ) }11 11( ) ,10 10(), 010 1(),0000{( 4 V n V n V ) }11 11( ) ,11 01( ) ,11 00() ,10 11( ) ,10 10() ,10 01( ) ,10 00( ), 011 1(), 010 1(), 010 0(),0 011 (),0 010 (),00 01( ),0000{( 4 =V Lecture 9 14 Some definitions… ... set. Example: {} .for basis a is )00 01( ),0 010 (), 010 0() ,10 00( 4 V {} . spans )10 01( ),0 011 () ,11 00(), 011 0() ,10 00( 4 V { } n G vvv ,,, 21 K = Lecture 9 15 Linear block codes Linear block code ... field : The set {0 ,1} , under modulo 2 binary addition and multiplication forms a field. Binary field is also called Galois field, GF(2). 011 10 1 11 0 000 =⊕ =⊕ =⊕ =⊕ 11 1 0 01 010 000 =⋅ =⋅ =⋅ =⋅...