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genMinDisIdeal -- generalized minimum distance function of an ideal

Description

Returns the value of the generalized minimum distance function (GMDF) of the ideal I on the parameters d and r. The GMDF generalizes the Hamming weights of Reed-Muller-type codes. The integers d and r indique that the function is computing the degree of the ideal generated by r-tuples of polynomials of degree at most d that are linearly independent modulo the ideal I. More information about the GMDF can be found in Definition 1.1 at https://arxiv.org/pdf/1812.06529v1.pdf.

i1 : K=ZZ/3;
i2 : R=K[t1,t2,t3,t4,t5,t6];
i3 : I=ideal(t1*t6-t3*t4,t2*t6-t3*t5);

o3 : Ideal of R
i4 : genMinDisIdeal(1,1,I)

o4 = 3

Ways to use genMinDisIdeal:

  • genMinDisIdeal(ZZ,ZZ,Ideal)

For the programmer

The object genMinDisIdeal is a method function.


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/CodingTheory.m2:3925:0.