New Non-Binary Quantum Codes Derived From a Class of Linear Codes

New Binary Linear Codes

Codes Derived from Binary Goppa Codes

We present a new family of binary codes derived from the family of classical Goppa codes. We generalize properties of Goppa codes to this family and deduce bounds on the dimension and on the minimum distance, and the existence of a polynomial-time decoding algorithm up to a constructed error-correcting capability. Asymptotically these codes have the same parameters as Goppa codes.

New binary linear codes from algebraic curves

Many new binary linear codes (compared with Brouwer’s table) are found from a construction based on algebraic curves over finite fields.

New quantum MDS codes derived from constacyclic codes

Quantum error-correcting codes play an important role in both quantum communication and quantum computation. It has experienced a great progress since the establishment of the connections between quantum codes and classical codes (see [4]). It was shown that the construction of quantum codes can be reduced to that of classical linear error-correcting codes with certain self-orthogonality proper...

A New Class of Binary Constant Weight Codes Derived by Groups of Linear Fractional Mappings

Let A(n, d, w) denote the maximum possible number of code words in binary (n, d, w) constant weight codes. For smaller instances of (n, d, w)s, many improvements have occurred over the decades. However, unknown instances still remain for larger (n, d, w)s (for example, those of n > 30 and d > 10). In this paper, we propose a new class of binary constant weight codes that fill in the remaining b...