Computation of minimum Hamming weight for linear codes. (English) Zbl 1455.94224
Summary: In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free \(R\)-submodules of a finite quasi-Frobenius ring \(R\) which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Gröbner basis and we show that under certain conditions a linear code takes the maximum of minimum Hamming weight.
MSC:
| 94B05 | Linear codes (general theory) |
| 94B65 | Bounds on codes |
| 13P10 | Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |
| 11T71 | Algebraic coding theory; cryptography (number-theoretic aspects) |
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