Some Punctured Codes of Several Families of Binary Linear Codes

Normality of some binary linear codes

We show that all binary codes of lengths 16, 17 and 18, or redundancy 10, are normal. These results have applications in the construction of codes that attain t[n, k], the smallest covering radius of any binary linear code.

Duality for Several Families of Evaluation Codes

We consider generalizations of Reed-Muller codes, toric codes, and codes from certain plane curves, such as those defined by norm and trace functions on finite fields. In each case we are interested in codes defined by evaluating arbitrary subsets of monomials, and in identifying when the dual codes are also obtained by evaluating monomials. We then move to the context of order domain theory, i...

New Binary Linear Codes

Binary Linear Block Codes

On the properness of some optimal binary linear codes and their dual codes

A linear code is said to be proper in error detection over a symmetric memoryless channel if its undetected error probability is an increasing function of the channel symbol error probability. A proper code performs well in error detection in the sense that the better the channel, the better the performance, which makes the code appropriate for use in channels where the symbol error probability...