Pure resolutions, linear codes, and Betti numbers

Armenoff, 2015 Assmus, 1992, Designs and Their Codes, vol. 103 Ashikhmin, 1998, Minimal vectors in linear codes, IEEE Trans. Inf. Theory, 44, 2010, 10.1109/18.705584 Björner, 1992, The homology and shellability of matroids and geometric lattices, vol. 40, 226 Boij, 2008, Graded Betti numbers of Cohen-Macaulay modules and the multiplicity conjecture, J. Lond. Math. Soc., 78, 85, 10.1112/jlms/jdn013 Bonisoli, 1984, Every equidistant linear code is a sequence of dual Hamming codes, Ars Comb., 18, 181 Bose, 1966, Hermitian varieties in a finite projective space PG(N,q2), Can. J. Math., 18, 1161, 10.4153/CJM-1966-116-0 Calderbank, 1986, The geometry of two-weight codes, Bull. Lond. Math. Soc., 18, 97, 10.1112/blms/18.2.97 Chakravarti, 1971, Some properties and applications of Hermitian varieties in a finite projective space PG(N,q2) in the construction of strongly regular graphs (two-class association schemes) and block designs, J. Comb. Theory, Ser. B, 11, 268, 10.1016/0095-8956(71)90037-2 Delsarte, 1970, On generalized Reed-Muller codes and their relatives, Inf. Control, 16, 403, 10.1016/S0019-9958(70)90214-7 Dembowski, 1968, Finite Geometries, vol. 44 Denniston, 1969, Some maximal arcs in finite projective planes, J. Comb. Theory, 6, 317, 10.1016/S0021-9800(69)80095-5 2013, vol. 18 Herzog, 1984, On the Betti numbers of finite pure and linear resolutions, Commun. Algebra, 12, 1627, 10.1080/00927878408823070 Johnsen, 2015 Johnsen, 2013, Hamming weights and Betti numbers of Stanley-Reisner rings associated to matroids, Appl. Algebra Eng. Commun. Comput., 24, 73, 10.1007/s00200-012-0183-7 Johnsen, 2014, Stanley-Reisner resolution of constant weight codes, Des. Codes Cryptogr., 72, 471, 10.1007/s10623-012-9767-2 Johnsen, 2016, A generalization of weight polynomials to matroids, Discrete Math., 339, 632, 10.1016/j.disc.2015.10.005 Jurrius, 2009, Extended and generalized weight enumerators, 76 Liu, 2010, Notes on the value function, Des. Codes Cryptogr., 54, 11, 10.1007/s10623-009-9305-z Karpova, 2015 Provan, 1977 Stanley, 1977, Cohen-Macaulay complexes, 51 Tsfasman, 2007, Algebraic Geometric Codes: Basic Notions, vol. 139 Wei, 1991, Generalized Hamming weights for linear codes, IEEE Trans. Inf. Theory, 37, 1412, 10.1109/18.133259