Geometric Approach to<i>b</i>-Symbol Hamming Weights of Cyclic Codes

Symbol-pair codes were introduced by Cassuto and Blaum in 2010 to protect pair errors symbol-pair read channels. Recently Yaakobi, Bruck Siegel (2016) generalized this notion b-symbol order consider consecutive b for a prescribed integer ? 2, they gave constructions decoding algorithms. Cyclic considered various authors as candidates established minimum distance bounds on (certain) cyclic codes. In paper we use algebraic curves over finite fields obtain tight lower upper Hamming weights of arbitrary F q . Here 2 is an positive \mathbb field. We also present stability theorem code C dimension k length n: the weight enumerator same k-symbol if ? n-1. Moreover, give improved some related irreducible Throughout n coprime q.