A new class of codes for byte organized systems from algebraic curves

A new class of linear codes over GF(q) for byte organized systems from algebraic curves is proposed. Here, an element in GF(q) is called a symbol and “byte” denotes a q-ary sequence of length b⩾2. A codeword in the code is composed of n bytes of byte-length b, thus, the code-length is nb, where N:=nb. These codes have the capability of correcting any error that corrupts both t₁ bytes and t₂ symbols within another byte where t₂<b. We call such a code a t₁ byte and t₂ symbol error correcting code, or a (t₁Bt₂S)EC code. Moreover, we refer to an error that corrupts both t₁ bytes and t₂ symbols within another byte as a t₁ byte and t₂ symbol error