Optimal Binary Linear Codes From Maximal Arcs

Binary Optimal Linear Rate 1/2 Codes

Binary Linear Codes with Optimal Scaling and Quasi-Linear Complexity

We present the first family of binary codes that attains optimal scaling and quasi-linear complexity, at least for the binary erasure channel (BEC). In other words, for any fixed δ > 0, we provide codes that ensure reliable communication at rates within ε > 0 of the Shannon capacity with block length n = O(1/ε2+δ), construction complexity Θ(n), and encoding/decoding complexity Θ(n log n). Furth...

On Linear Codes from Maximal Curves

Some linear codes associated to maximal algebraic curves via Feng-Rao construction [3] are investigated. In several case, these codes have better minimum distance with respect to the previously known linear codes with same length and dimension.

Some Optimal Codes From Designs

The binary and ternary codes spanned by the rows of the point by block incidence matrices of some 2-designs and their complementary and orthogonal designs are studied. A new method is also introduced to study optimal 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.