1 + 1 ] ( Eqn . ? 1 )
and encoding of the three bits D₀, D₁, D₂ may be obtained by multiplying the data bits by rows 2-4 of the Hadamard matrix H₄ to obtain four output values. In such an embodiment, each row of the rows 2-4 of the matrix of Eqn. 1 corresponds to a respective sub-channel vector of a plurality of sub-channel vectors. Each sub-channel vector being modulated, or weighted, by a respective data bit (taking values of +1 or ?1) corresponds to a modulated sub-channel. A sum of all of the modulated sub-channels produces a codeword of a vector signaling code. In the word-oriented view, the three-bit data word D<2:0> is multiplied by rows 2-4 of the above matrix to encode the data into a four value codeword composed of values [A, B, C, D]. An offset may be added to each codeword value for ease in transmission along the multi-wire bus medium. Because the first “all-ones” row of the matrix is not used, the resulting codewords of the ENRZ code are balanced, all symbols of a given codeword summing to zero (or a constant when an offset is added), and are either permutations of the vector [+1, ??, ??, ??] or [?1, +?, +?, +?]. Thus, physical wire signals corresponding to a series of ENRZ codewords may take on four distinct values.